It is currently 16 Jan 2018, 09:48

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

To furnish a room in a model home, an interior decorator is

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

2 KUDOS received
Manager
Manager
User avatar
Joined: 10 Jul 2009
Posts: 126

Kudos [?]: 192 [2], given: 60

Location: Ukraine, Kyiv
To furnish a room in a model home, an interior decorator is [#permalink]

Show Tags

New post 01 Nov 2009, 08:50
2
This post received
KUDOS
14
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

79% (01:13) correct 21% (01:14) wrong based on 396 sessions

HideShow timer Statistics

To furnish a room in model home, an interior decorator is to select 2 chairs and 2 tables from a collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables are in the warehouse?

A. 6
B. 8
C. 10
D. 15
E. 30

[Reveal] Spoiler:
The answer is A. BUT!
what is the next step in the process?

5C2*nC2=150
10*nC2=150
nC2=15

n! / 2!*(n-2)! = 15
n!=30(n-2)!

stuck here. what do I need to do next in order to arrive to the answer choice A, 6 tables?

award kudos for good explanation
[Reveal] Spoiler: OA

_________________

Never, never, never give up

Kudos [?]: 192 [2], given: 60

Expert Post
4 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43295

Kudos [?]: 139194 [4], given: 12778

Re: To furnish a room in a model home, an interior decorator is [#permalink]

Show Tags

New post 01 Nov 2009, 09:06
4
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
barakhaiev wrote:
HI!

This question has already been posted several times, but still I did not understand the reasoning:

To furnish a room in a model home, an interior decorator is to select 2 chairs from a collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables are in the warehouse?

6
8
10
15
30

The answer is A. BUT!
what is the next step in the process?

5C2*nC2=150
10*nC2=150
nC2=15

n! / 2!*(n-2)! = 15
n!=30(n-2)!

stuck here. what do I need to do next in order to arrive to the answer choice A, 6 tables?

award kudos for good explanation


You've done most of the work right, next step:
\(\frac{n!}{2!*(n-2)!}=15\). \((n-2)!\) will just cancel out and will get:

\(\frac{(n-1)*n}{2!}=15\) --> \((n-1)*n=30\) --> \(n=6\)

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 139194 [4], given: 12778

Manager
Manager
User avatar
Joined: 10 Jul 2009
Posts: 126

Kudos [?]: 192 [0], given: 60

Location: Ukraine, Kyiv
Re: To furnish a room in a model home, an interior decorator is [#permalink]

Show Tags

New post 01 Nov 2009, 09:20
Thank you very much, Bunuel, for such a fast and detailed response. Kudos, as promised!
_________________

Never, never, never give up

Kudos [?]: 192 [0], given: 60

Retired Moderator
User avatar
Joined: 02 Sep 2010
Posts: 792

Kudos [?]: 1252 [0], given: 25

Location: London
GMAT ToolKit User Reviews Badge
Re: To furnish a room in a model home, an interior decorator is [#permalink]

Show Tags

New post 23 Sep 2010, 11:04
udaymathapati wrote:
Pls help to solve this problem.

Attachment:
Image3.JPG


No of combinations = C(5,2) * C(x,2) = 10 * x(x-1)/2 =150
Where x is the number of tables

So x(x-1)/2 = 15
x(x-1) = 30

And we know x is an integer

=> x=6
_________________

Math write-ups
1) Algebra-101 2) Sequences 3) Set combinatorics 4) 3-D geometry

My GMAT story

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 1252 [0], given: 25

Manager
Manager
User avatar
Joined: 13 Jul 2010
Posts: 159

Kudos [?]: 98 [0], given: 7

Re: To furnish a room in a model home, an interior decorator is [#permalink]

Show Tags

New post 27 Sep 2010, 06:38
Shrouded how did you arrive at x(x-1)/2 for c(x,2)? shouldn't this be x!/2!(x-2)! ? I am having trouble following how you arrived at x(x-1)/2? Please advise, thank you!

Kudos [?]: 98 [0], given: 7

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43295

Kudos [?]: 139194 [0], given: 12778

Re: To furnish a room in a model home, an interior decorator is [#permalink]

Show Tags

New post 27 Sep 2010, 06:58
Expert's post
2
This post was
BOOKMARKED
gettinit wrote:
Shrouded how did you arrive at x(x-1)/2 for c(x,2)? shouldn't this be x!/2!(x-2)! ? I am having trouble following how you arrived at x(x-1)/2? Please advise, thank you!


\(C(x,2)=\frac{x!}{2!*(x-2)!}=\frac{(x-2)!*(x-1)*x}{2!*(x-2)!}\) so you can reduce by \((x-2)!\) and you'll get \(\frac{(x-1)x}{2}\).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 139194 [0], given: 12778

Senior Manager
Senior Manager
avatar
Joined: 06 Jun 2009
Posts: 327

Kudos [?]: 87 [0], given: 0

Location: USA
WE 1: Engineering
Re: To furnish a room in a model home, an interior decorator is [#permalink]

Show Tags

New post 27 Sep 2010, 07:13
Out of curiosity

Why didn't we take different possible arrangements where order of selection is important (permutation). For example, if we have two chairs (A&B) and two tables (X&Y) selected from the warehouse, we can arrange them as AX & BY and AY & BX. Was this because of the fact that it was given that there are 150 different combinations ?
_________________

All things are possible to those who believe.

Kudos [?]: 87 [0], given: 0

Senior Manager
Senior Manager
avatar
Joined: 06 Jun 2009
Posts: 327

Kudos [?]: 87 [0], given: 0

Location: USA
WE 1: Engineering
Re: To furnish a room in a model home, an interior decorator is [#permalink]

Show Tags

New post 27 Sep 2010, 07:16
gettinit wrote:
Shrouded how did you arrive at x(x-1)/2 for c(x,2)? shouldn't this be x!/2!(x-2)! ? I am having trouble following how you arrived at x(x-1)/2? Please advise, thank you!


x ! / [2!(x-2)!] = [(x-2)!(x-1)(x)]/[2!(x-2)!] = [(x-1)(x)]/2
_________________

All things are possible to those who believe.

Kudos [?]: 87 [0], given: 0

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43295

Kudos [?]: 139194 [0], given: 12778

Re: To furnish a room in a model home, an interior decorator is [#permalink]

Show Tags

New post 27 Sep 2010, 07:31
adishail wrote:
Out of curiosity

Why didn't we take different possible arrangements where order of selection is important (permutation). For example, if we have two chairs (A&B) and two tables (X&Y) selected from the warehouse, we can arrange them as AX & BY and AY & BX. Was this because of the fact that it was given that there are 150 different combinations ?


Decorator is to select 2 different chairs out of 5 and 2 different tables out of n. Now, two selections {C1, C2, T1, T2} and {C2, C1, T2, T1,} are the same for decorator as there are the same chairs and tables in both of them. So the order in which the items are taken is not considered.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 139194 [0], given: 12778

Senior Manager
Senior Manager
avatar
Joined: 06 Jun 2009
Posts: 327

Kudos [?]: 87 [0], given: 0

Location: USA
WE 1: Engineering
Re: To furnish a room in a model home, an interior decorator is [#permalink]

Show Tags

New post 27 Sep 2010, 07:54
Bunuel wrote:
adishail wrote:
Out of curiosity

Why didn't we take different possible arrangements where order of selection is important (permutation). For example, if we have two chairs (A&B) and two tables (X&Y) selected from the warehouse, we can arrange them as AX & BY and AY & BX. Was this because of the fact that it was given that there are 150 different combinations ?


Decorator is to select 2 different chairs out of 5 and 2 different tables out of n. Now, two selections {C1, C2, T1, T2} and {C2, C1, T2, T1,} are the same for decorator as there are the same chairs and tables in both of them. So the order in which the items are taken is not considered.

Hope it's clear.


Yes. I understood your explanation.

However, I am talking about a case where we would have {C1T1, C2T2, and C1T2, C2T1} since these two can be considered different arrangements. But I think I somehow got stuck with the idea of making a set of a chair and table.

I guess if they would have worded it something like - If 150 different sets of tables and chair are possible ...........then order would have been important. Is that correct Bunuel ? And in that case we would have taken COMBINATION for chairs and PERMUTATION for tables or vice versa because if we would have taken PERMUTATION for both tables an chairs, then we would have ended up with two identical cases like {C1T1, C2T2} and {C2T2, C1T1}.
_________________

All things are possible to those who believe.

Kudos [?]: 87 [0], given: 0

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43295

Kudos [?]: 139194 [0], given: 12778

Re: To furnish a room in a model home, an interior decorator is [#permalink]

Show Tags

New post 27 Sep 2010, 08:23
adishail wrote:
Bunuel wrote:
adishail wrote:
Out of curiosity

Why didn't we take different possible arrangements where order of selection is important (permutation). For example, if we have two chairs (A&B) and two tables (X&Y) selected from the warehouse, we can arrange them as AX & BY and AY & BX. Was this because of the fact that it was given that there are 150 different combinations ?


Decorator is to select 2 different chairs out of 5 and 2 different tables out of n. Now, two selections {C1, C2, T1, T2} and {C2, C1, T2, T1,} are the same for decorator as there are the same chairs and tables in both of them. So the order in which the items are taken is not considered.

Hope it's clear.


Yes. I understood your explanation.

However, I am talking about a case where we would have {C1T1, C2T2, and C1T2, C2T1} since these two can be considered different arrangements. But I think I somehow got stuck with the idea of making a set of a chair and table.

I guess if they would have worded it something like - If 150 different sets of tables and chair are possible ...........then order would have been important. Is that correct Bunuel ? And in that case we would have taken COMBINATION for chairs and PERMUTATION for tables or vice versa because if we would have taken PERMUTATION for both tables an chairs, then we would have ended up with two identical cases like {C1T1, C2T2} and {C2T2, C1T1}.


You are right we are not told to pair a chair with table. Also I don't think that changing the word "combination" with "set" would make a difference, the question is clearly talking about the different selections of 2 chairs and 2 tables.

If we were interested in such pairs then you should notice that one particular selection of 2 chairs and 2 tables {C1, C2, T1, T2} can give 2 different pairs of chair/table: {C1/T1, C2/T2} or {C1/T2, C2/T1}.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 139194 [0], given: 12778

Senior Manager
Senior Manager
avatar
Joined: 06 Jun 2009
Posts: 327

Kudos [?]: 87 [0], given: 0

Location: USA
WE 1: Engineering
Re: To furnish a room in a model home, an interior decorator is [#permalink]

Show Tags

New post 27 Sep 2010, 08:35
Quote:
If we were interested in such pairs then you should notice that one particular selection of 2 chairs and 2 tables {C1, C2, T1, T2} can give 2 different pairs of chair/table: {C1/T1, C2/T2} or {C1/T2, C2/T1}.


Correct.

In that case, either the total combinations can be

1) multiplied by 2, or

2) find Permutation for both items and then divide by 2 to eliminate the identical set like {C1,T1 & C2,T2} and {C2,T2 & C1,T1}

Is that right ?
_________________

All things are possible to those who believe.

Kudos [?]: 87 [0], given: 0

1 KUDOS received
Intern
Intern
avatar
Joined: 10 Oct 2010
Posts: 23

Kudos [?]: 24 [1], given: 1

Location: Texas
Re: To furnish a room in a model home, an interior decorator is [#permalink]

Show Tags

New post 11 Oct 2010, 02:42
1
This post received
KUDOS
barakhaiev wrote:
HI!

This question has already been posted several times, but still I did not understand the reasoning:

To furnish a room in a model home, an interior decorator is to select 2 chairs

Combo box arrangement for chairs
(_)(_)/2!

barakhaiev wrote:
and 2 tables from a colelction of chairs and tables in a warehouse that are all different from each other.

Combo box arrangement for chairs and tables
(_)(_)/2! * (_)(_)/2!

barakhaiev wrote:
If there are 5 chairs in the warehouse

Fill in combo box arrangement
(5)(4)/2! * (_)(_)/2!

barakhaiev wrote:
and if 150 different combinations are possible

(5)(4)/2! * (_)(_)/2! = 150

barakhaiev wrote:
, how many tables in the warehouse?

(5)(4)/2! * (Tables)(Tables - 1)/2! = 150

Algebra
(Tables)(Tables - 1) = 150 * 2! * 2 ! / (5)(4) = 30 = 6*5
Tables = 6

Kudos [?]: 24 [1], given: 1

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43295

Kudos [?]: 139194 [2], given: 12778

Re: To furnish a room in model home, an interior decorator is to [#permalink]

Show Tags

New post 10 Dec 2010, 10:46
2
This post received
KUDOS
Expert's post
To furnish a room in model home, an interior decorator is to select 2 chairs and 2 tables from a collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables are in the warehouse?
A. 6
B. 8
C. 10
D. 15
E. 30

\(C^2_5*C^2_t=150\), where \(t\) is the # of tables --> \(C^2_5*C^2_t=150\) --> \(C^2_t=15\) --> \(\frac{t!}{2!(t-2)!}=15\) --> \((t-2)!\) will cancel out --> \((t-1)t=30\) --> \(t=6\).

Answer: A.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 139194 [2], given: 12778

1 KUDOS received
Manager
Manager
User avatar
Joined: 07 Oct 2010
Posts: 170

Kudos [?]: 187 [1], given: 10

Re: To furnish a room in model home, an interior decorator is to [#permalink]

Show Tags

New post 10 Dec 2010, 10:59
1
This post received
KUDOS
GMAT prep problem...
It should be solved like following
Suppose we have to select 2 tables from “X” tables
We have already given that we have to select 2 chairs form 5 and we total possible combinations are 150

Therefore,
5C2 * XC2 = 150
5*4/2 * X!/2!(X-2)! = 150
X!/2!(X-2)! = 15
X!/(X-2)! = 30
X(X-1)(X-2)! / (X-2)! = 30
X(X-1) = 30
X2 – X – 30 = 0
X2 – 6X + 5X – 30 = 0
X(X – 6) + 5(X – 6) = 0
(X – 6) (X + 5) = 0
X = 6 or X = -5
Negative value is not possible since we are calculating the number of tables
Therefore X = 6
Hence “A” is the answer

Kudos [?]: 187 [1], given: 10

Intern
Intern
avatar
Joined: 21 Feb 2015
Posts: 27

Kudos [?]: 10 [0], given: 23

To furnish a room in a model home, an interior decorator is [#permalink]

Show Tags

New post 26 Jul 2015, 16:39
Bunuel wrote:
gettinit wrote:
Shrouded how did you arrive at x(x-1)/2 for c(x,2)? shouldn't this be x!/2!(x-2)! ? I am having trouble following how you arrived at x(x-1)/2? Please advise, thank you!


\(C(x,2)=\frac{x!}{2!*(x-2)!}=\frac{(x-2)!*(x-1)*x}{2!*(x-2)!}\) so you can reduce by \((x-2)!\) and you'll get \(\frac{(x-1)x}{2}\).



Hi Bunuel,
I don't understand how you got (x-2)!*(x-1)*x in the numerator

Last edited by Rookie124 on 26 Jul 2015, 16:41, edited 1 time in total.

Kudos [?]: 10 [0], given: 23

Current Student
avatar
S
Joined: 20 Mar 2014
Posts: 2685

Kudos [?]: 1842 [0], given: 799

Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
To furnish a room in a model home, an interior decorator is [#permalink]

Show Tags

New post 26 Jul 2015, 17:00
mawus wrote:
Bunuel wrote:
gettinit wrote:
Shrouded how did you arrive at x(x-1)/2 for c(x,2)? shouldn't this be x!/2!(x-2)! ? I am having trouble following how you arrived at x(x-1)/2? Please advise, thank you!


\(C(x,2)=\frac{x!}{2!*(x-2)!}=\frac{(x-2)!*(x-1)*x}{2!*(x-2)!}\) so you can reduce by \((x-2)!\) and you'll get \(\frac{(x-1)x}{2}\).



Hi Bunuel,
I don't understand how you got (x-2)!*(x-1)*x in the numerator


Let me try to answer this question.

When you write:

\(C(x,y) = \frac{x!}{y!*(x-y)!}\)

Now substitute y =2 in the above equation:

\(C(x,2) = \frac{x!}{2!*(x-2)!}\)

Now any factorial, n! = n*(n-1)*(n-2).....1

Thus, x! = x*(x-1)*[(x-2)*(x-3).....1]

and particularly, [(x-2)*(x-3).....1] = (x-2)! ( we are doing this to cancel out (x-2)! in the denominator.

Finally, \(C(x,2) = \frac{x!}{2!*(x-2)!}\) ---> \(C(x,2) = \frac{x*(x-1)*(x-2)!}{2!*(x-2)!}\)

If these variables are creating confusion for you, take 4! = 4*3*2*1 ---> If x= 4, then x-1 =3, x-2 =2, ...etc. This is what Bunuel has done above.


If you are still having difficulties, for the above question,

150 = C(5,2) * C(n,2), where n= total number of tables in the warehouse.

\(C(5,2) = \frac{5!}{2!*3!} = \frac{5*4*3!}{2!*3!}\) = 10

Thus, C(n,2) = 150/10 = 15

Now, try the given answer choices to see which of the values when substituted for n gives you C(n,2) =15. n =6 will satisfy this equation.

Hope this helps.

Kudos [?]: 1842 [0], given: 799

Expert Post
1 KUDOS received
Target Test Prep Representative
User avatar
S
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1820

Kudos [?]: 1044 [1], given: 5

Re: To furnish a room in a model home, an interior decorator is [#permalink]

Show Tags

New post 18 Sep 2017, 04:50
1
This post received
KUDOS
Expert's post
barakhaiev wrote:
To furnish a room in model home, an interior decorator is to select 2 chairs and 2 tables from a collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables are in the warehouse?

A. 6
B. 8
C. 10
D. 15
E. 30


We are given that an interior decorator is to select 2 chairs and 2 tables from a collection of chairs and tables. We are also given that there are 5 chairs in the warehouse and 150 different possible combinations. We must determine the number of tables. We can let n = the number of tables and create the following equation:

5C2 x nC2 = 150

[(5 x 4)/2!] x [(n x n-1)/2!] = 150

20/2 x (n^2 – 1)/2 = 150

10 x (n^2 – 1)/2 = 150

(n^2 – 1)/2 = 15

n^2 – 1 = 30

n^2 – 1 – 30 = 0

(n – 6)(n + 5) = 0

n = 6 or n = -5.

Since n must be positive, the number of tables is 6.

Answer: A
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 1044 [1], given: 5

Re: To furnish a room in a model home, an interior decorator is   [#permalink] 18 Sep 2017, 04:50
Display posts from previous: Sort by

To furnish a room in a model home, an interior decorator is

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.