Mar 23 07:00 AM PDT  09:00 AM PDT Christina scored 760 by having clear (ability) milestones and a trackable plan to achieve the same. Attend this webinar to learn how to build trackable milestones that leverage your strengths to help you get to your target GMAT score. Mar 27 03:00 PM PDT  04:00 PM PDT Join a free live webinar and learn the winning strategy for a 700+ score on GMAT & the perfect application. Save your spot today! Wednesday, March 27th at 3 pm PST
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 24 May 2016
Posts: 141

In how many different ways can 8 people be seated in a room...
[#permalink]
Show Tags
11 Aug 2016, 02:42
Question Stats:
64% (02:02) correct 36% (01:51) wrong based on 193 sessions
HideShow timer Statistics
In how many different ways can 8 people be seated in a room with 10 chairs? A) 40,320 B) 181,440 C) 403,200 D) 1,814,400 E) 3,628,800 Please explain in detail your answer so that we can all follow it.
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 53770

In how many different ways can 8 people be seated in a room...
[#permalink]
Show Tags
11 Aug 2016, 02:47
EBITDA wrote: In how many different ways can 8 people be seated in a room with 10 chairs?
A) 40,320 B) 181,440 C) 403,200 D) 1,814,400 E) 3,628,800
Please explain in detail your answer so that we can all follow it. \(10P8 = \frac{10!}{(108)!} = 1,814,400\), choosing 8 out of 10, when order matters. Answer: D.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 01 Jun 2016
Posts: 5

Re: In how many different ways can 8 people be seated in a room...
[#permalink]
Show Tags
11 Aug 2016, 04:13
EBITDA wrote: In how many different ways can 8 people be seated in a room with 10 chairs?
A) 40,320 B) 181,440 C) 403,200 D) 1,814,400 E) 3,628,800
Please explain in detail your answer so that we can all follow it. Order doesn't matter With 10 chairs and only 8 to seat 8! Number of ways the 8 can seat on the chair 10C2  Number of ways the 2 empty sits can be vary with the 8 seated 8! * 10C2 = 1,814,400 Answer  D



Math Expert
Joined: 02 Aug 2009
Posts: 7424

Re: In how many different ways can 8 people be seated in a room...
[#permalink]
Show Tags
11 Aug 2016, 04:21
EBITDA wrote: In how many different ways can 8 people be seated in a room with 10 chairs?
A) 40,320 B) 181,440 C) 403,200 D) 1,814,400 E) 3,628,800
Please explain in detail your answer so that we can all follow it. Hi, The logic is Let the first person sit in one out of 10... So next will have 9 to choose from and next 8 and so on.. So total ways 10*9*8*7*6*5*4*3 which is same as 10P8... D
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html 4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentageincreasedecreasewhatshouldbethedenominator287528.html
GMAT Expert



Manager
Joined: 24 May 2016
Posts: 141

In how many different ways can 8 people be seated in a room...
[#permalink]
Show Tags
11 Aug 2016, 04:28
chisicheiWhen you say that order does not matter, I presume that you mean that the order among the empty seats does not matter. Am I right?



Intern
Joined: 29 Jun 2016
Posts: 43

Re: In how many different ways can 8 people be seated in a room...
[#permalink]
Show Tags
11 Aug 2016, 11:23
Order doesnot matter
no of ways of selecting 8 chairs of 10 chairs =10C8 ways In these 8 chairs 8 people can be seated in 8! ways
SO total =10C8 *8! which is also equal to 10P8



Director
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 534
Location: Bangladesh
Concentration: Finance, Leadership
GPA: 2.81
WE: Business Development (Real Estate)

Re: In how many different ways can 8 people be seated in a room...
[#permalink]
Show Tags
11 Aug 2016, 13:00
chisichei wrote: EBITDA wrote: In how many different ways can 8 people be seated in a room with 10 chairs?
A) 40,320 B) 181,440 C) 403,200 D) 1,814,400 E) 3,628,800
Please explain in detail your answer so that we can all follow it. Order doesn't matter With 10 chairs and only 8 to seat 8! Number of ways the 8 can seat on the chair 10C2  Number of ways the 2 empty sits can be vary with the 8 seated 8! * 10C2 = 1,814,400 Answer  D Nice Solution But I believe order matters and order among empty seat also matters here and you made the solution considering all orders for this problem. Did I missed something?
_________________
Md. Abdur Rakib
Please Press +1 Kudos,If it helps Sentence CorrectionCollection of Ron Purewal's "elliptical construction/analogies" for SC Challenges



Retired Moderator
Status: The best is yet to come.....
Joined: 10 Mar 2013
Posts: 495

Re: In how many different ways can 8 people be seated in a room...
[#permalink]
Show Tags
03 Feb 2017, 09:45
In how many different ways can 12 people be seated in a room with 10 chairs? Is it 12C10*10!?
_________________
Hasan Mahmud



Senior Manager
Joined: 03 Apr 2013
Posts: 274
Location: India
Concentration: Marketing, Finance
GPA: 3

In how many different ways can 8 people be seated in a room...
[#permalink]
Show Tags
17 Jun 2017, 00:51
EBITDA wrote: In how many different ways can 8 people be seated in a room with 10 chairs?
A) 40,320 B) 181,440 C) 403,200 D) 1,814,400 E) 3,628,800
Please explain in detail your answer so that we can all follow it. Here's two more ways to think about this one. 1. There are in total 10 things to be arranged, i.e. 8 people and 2 gaps(which are similar). Number of ways of arranging 10 things out of which 2 are similar \(\frac{10!}{2}\) Answer (D) 2. as there are 10 chairs and 8 people, we will have to first choose which 8 chairs to fill. After we have chosen our chairs, we can arrange the people. \(10C8 * 8!\) This can also be imagined in another way, we have to choose 2 chairs to leave empty. And then we have to arrange the people in the remaining 8 chairs. \(10C2 * 8!\) Answer (D)
_________________
Spread some love..Like = +1 Kudos



Intern
Joined: 08 Jan 2017
Posts: 15
GPA: 3

Re: In how many different ways can 8 people be seated in a room...
[#permalink]
Show Tags
17 Jun 2017, 04:15
It is very clearly 10C8*8!= 10*9*8*7*6*5*4*3 We don't need to calculate the above. Here's the trick
1. How many number of zeros can this have? Number of zeros= highest power of 10, which is equal to 2 A and B eliminated
The remaining three choices have different digits before zero, thus if we can figure out the digit we will get the answer. The digit before zero is 4. Thus D is the answer
Kudos if this is helpful



Intern
Joined: 30 Mar 2017
Posts: 38
Location: United States (FL)

Re: In how many different ways can 8 people be seated in a room...
[#permalink]
Show Tags
03 Jul 2017, 03:07
I'm not sure if the calculation portion is within the scope of the GMAT but given the spread of the numbers, it is definitely doable.
The trick is to get everything to the power of base 10. I won't go through the entire exercise but I will start with this example: 10!/2! = 10*9*8*7*6*5*4*3*2 can be rewritten as: 10*10*9*8*7*6*_*4*3*_* Notice the 2 and 5 missing  they were actually multiplied to get another 10. Here is one more (less straightforward step): 10*10*10*10*1.12*9*6*2*3 In the step I just wrote out, we multiplied 7 * 8 * 2(from the 4) to get 112 which we rewrote as 1.12 * 100(10*10)



Manager
Joined: 01 Aug 2017
Posts: 189
Location: India
Concentration: General Management, Leadership
GPA: 3.4
WE: Information Technology (Computer Software)

Re: In how many different ways can 8 people be seated in a room...
[#permalink]
Show Tags
12 Sep 2018, 00:00
EBITDA wrote: In how many different ways can 8 people be seated in a room with 10 chairs?
A) 40,320 B) 181,440 C) 403,200 D) 1,814,400 E) 3,628,800
Please explain in detail your answer so that we can all follow it. Selecting 8 seats on which 8 people would be seated  10C8. This can be arranged in 8! ways. Answer = \(10C8 * 8! = 1,814,400\)
_________________
If it helps you please press Kudos!
Thank You Sudhanshu




Re: In how many different ways can 8 people be seated in a room...
[#permalink]
12 Sep 2018, 00:00






