GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 14 Oct 2019, 11:32

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

A certain club has 20 members. What is the ratio of the memb

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

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
B
Joined: 26 Mar 2017
Posts: 106
Re: A certain club has 20 members. What is the ratio of the memb  [#permalink]

Show Tags

New post 15 Jun 2017, 10:00
Bunuel wrote:
bakfed wrote:
brinng back an old post.

I somehow can't get 20C5/20C4 to be 16/5; I keep on getting 8/5

Also, for this question, why can't we just do the following:
(20*19*18*17*16)/(20*19*18*17) = 16/1?


\(\frac{C^5_{20}}{C^4_{20}}=\frac{20!}{15!*5!}*\frac{16!*4!}{20!}=\frac{16}{5}\)

Second question:

20*19*18*17*16 does not give you # of 5 member committees out of 20. You need to divide this by 5! to get rid of the repetitions (factorial correction). The same for 20*19*18*17, you should divide this by 4!.

Take another example: how many committees of 2 can be formed out of A, B and C?

AB
AC
BC
Only 3, which is \(C^2_3=3\).

But the way you are doing you'd get 3*2=6. This number has repetitions so we should divide it by 2! --> 6/2!=3.

Hope it's clear.



hey I got the correct answer but was just wondering why the members have to be different, i.e. why we are using combinations ?

What am I missing here ? :cry:
_________________
I hate long and complicated explanations!
Intern
Intern
avatar
B
Joined: 31 Jan 2017
Posts: 8
A certain club has 20 members. What is the ratio of the memb  [#permalink]

Show Tags

New post 22 Jun 2018, 13:57
So the formula that we have to remember when it comes to combinatorics in which case sequence does not matter is this:

n!
---------
(k!)((n-k)!)

in which n is the total number of units and k is the number of units per set.

--------------------------------------------------------------------------


So in the case of our problem, n = 20 and for the first set k = 5. In the second set k = 4. So putting it all together, it looks like this:

20!
---------
5!((20-5)!)
--------------
20!
---------
4!((20-4)!)



Simplify:

20!
---------
5!((15!)
-------------
20!
---------
4!((16!)


Simplify:

20! 4!(16!)
------- x -------
5!(15!) 20!



Simplify:

4!(16!)
-------
5!(15!)


Solve:

4 * 3 * 2 * 1 * 16 * 15! 16
-------------------- --> ---- --> or 16 : 5
5 * 4 * 3 * 2 * 1 * 15! 5

The answer is C.
CEO
CEO
User avatar
V
Joined: 12 Sep 2015
Posts: 3996
Location: Canada
Re: A certain club has 20 members. What is the ratio of the memb  [#permalink]

Show Tags

New post 28 Feb 2019, 07:08
Top Contributor
milind1979 wrote:
A certain club has 20 members. What is the ratio of the member of 5-member committees that can be formed from the members of the club to the number of 4-member committees that can be formed from the members of the club?

A. 16 to 1
B. 15 to 1
C. 16 to 5
D. 15 to 6
E. 5 to 4


5-member committees
Since the order in which we select the committee members does not matter, we can use COMBINATIONS
We can select 5 people from 20 people in 20C5 ways
20C5 = (20)(19)(18)(17)(16)/(5)(4)(3)(2)(1)

4-member committees
Since the order in which we select the committee members does not matter, we can use COMBINATIONS
We can select 4 people from 20 people in 20C4 ways
20C4 = (20)(19)(18)(17)/(4)(3)(2)(1)

The RATIO = (20)(19)(18)(17)(16)/(5)(4)(3)(2)(1)]/[(20)(19)(18)(17)/(4)(3)(2)(1)]
= (20)(19)(18)(17)(16)/(5)(4)(3)(2)(1)][(4)(3)(2)(1)/(20)(19)(18)(17)]
=(20)(19)(18)(17)(16)(4)(3)(2)(1)/(20)(19)(18)(17)(5)(4)(3)(2)(1)
=(20)(19)(18)(17)(16)(4)(3)(2)(1)/(20)(19)(18)(17)(5)(4)(3)(2)(1)
=16/5

Answer: C

Cheers,
Brent

RELATED VIDEO FROM MY COURSE

_________________
Test confidently with gmatprepnow.com
Image
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8043
Location: United States (CA)
Re: A certain club has 20 members. What is the ratio of the memb  [#permalink]

Show Tags

New post 04 Mar 2019, 20:18
milind1979 wrote:
A certain club has 20 members. What is the ratio of the member of 5-member committees that can be formed from the members of the club to the number of 4-member committees that can be formed from the members of the club?

A. 16 to 1
B. 15 to 1
C. 16 to 5
D. 15 to 6
E. 5 to 4


The ratio is the following:

(20C5)/(20C4) = [(20 x 19 x 18 x 17 x 16)/5!]/[(20 x 19 x 18 x 17)/4!]

= [(20 x 19 x 18 x 17 x 16)/5!] x [4!/(20 x 19 x 18 x 17)]

= 16/5

Answer: C
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Bot
Re: A certain club has 20 members. What is the ratio of the memb   [#permalink] 04 Mar 2019, 20:18

Go to page   Previous    1   2   [ 24 posts ] 

Display posts from previous: Sort by

A certain club has 20 members. What is the ratio of the memb

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





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