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

 It is currently 20 Oct 2019, 22:06

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

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

In how many ways can a group of 15 friends be seated round 2 tables if

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

Hide Tags

Current Student
Joined: 22 Jul 2014
Posts: 120
Concentration: General Management, Finance
GMAT 1: 670 Q48 V34
WE: Engineering (Energy and Utilities)
In how many ways can a group of 15 friends be seated round 2 tables if  [#permalink]

Show Tags

14 Sep 2014, 07:51
2
14
00:00

Difficulty:

15% (low)

Question Stats:

76% (01:30) correct 24% (01:45) wrong based on 92 sessions

HideShow timer Statistics

In how many ways can a group of 15 friends be seated round 2 tables if one of the tables can seat 10 and the other can seat 5 people?

A) 15C5 * 9! *4!
B) 15C3 * 8! *3!
C) 15C4 * 9! *3!
D) 15C2 * 10! *3!
E) 16C5 * 10! *4!

Source: 4gmat

Manager
Joined: 21 Jul 2014
Posts: 119
Re: In how many ways can a group of 15 friends be seated round 2 tables if  [#permalink]

Show Tags

14 Sep 2014, 08:21
3
2
alphonsa wrote:
In how many ways can a group of 15 friends be seated round 2 tables if one of the tables can seat 10 and the other can seat 5 people?

A) 15C5 * 9! *4!
B) 15C3 * 8! *3!
C) 15C4 * 9! *3!
D) 15C2 * 10! *3!
E) 16C5 * 10! *4!

Source: 4gmat

This is a great question to test your understanding of counting methods. It tricks you into thinking that you'll have to do a lot of complex math, but if you apply a method I like to call "Half Baked" you can find the correct answer very shortly. (Half baked basically means only solve the problem to the extent you need to eliminate all of the wrong answers.)

First, I start by building the first table. I'm choosing 10 people from a group of 15: 15C10. However, none of my answer choices reflect this. So I apply another principle that lets me rephrase the answer. If you have the Official Guide, look at the last sentence of the Counting Methods section (4.1.10) where it says nCk = nC(n-k). This makes sense because if I start with the OTHER table, I would have gotten 15C5 and ended up with the same scenario.

This means that 15C10 = 15C5.

Given that answer choice A is the only one that matches this start, I would select it and move on.

But you might be interested in knowing more about how to completely solve the problem.

Having established the first part of the answer, now I'm interested in knowing what order each person will sit in at the table.

So I have a table of 10 and a table of 5, and I need to order people around each table. The trap answer here is 10! and 5!. However, remember that in a circular table, there is a unique circumstance where it matters who is sitting on either side of the person, not necessarily what seat they occupy. Therefore, if everyone in the group shifts one seat to the left, then it is still the same table arrangement.

Instead of 10! and 5!, you account for the rotation around the table by reducing the factorial number by 1, getting 9! and 4! as the answer.

So your final answer becomes 15C5 * 9! * 4!.
General Discussion
Manager
Status: I am not a product of my circumstances. I am a product of my decisions
Joined: 20 Jan 2013
Posts: 108
Location: India
Concentration: Operations, General Management
GPA: 3.92
WE: Operations (Energy and Utilities)
Re: In how many ways can a group of 15 friends be seated round 2 tables if  [#permalink]

Show Tags

14 Sep 2014, 08:31
2
alphonsa wrote:
In how many ways can a group of 15 friends be seated round 2 tables if one of the tables can seat 10 and the other can seat 5 people?

A) 15C5 * 9! *4!
B) 15C3 * 8! *3!
C) 15C4 * 9! *3!
D) 15C2 * 10! *3!
E) 16C5 * 10! *4!

Source: 4gmat

IMO ans is A

Explanation

10 people can be selected from 15 people in 15C10 ways.
Remaining 5 people can be selected from 5 people in 5C5 ways.

Now, arranging 10 people on a round table = (10-1) ! = 9!
Arranging 5 people on a round table = (5-1) ! = 4!

Hence, total number of ways = 15C10 * 9! * 5C5 * 4!
= 15C5 * 9! * 4!

15C10
Manager
Status: I am not a product of my circumstances. I am a product of my decisions
Joined: 20 Jan 2013
Posts: 108
Location: India
Concentration: Operations, General Management
GPA: 3.92
WE: Operations (Energy and Utilities)
Re: In how many ways can a group of 15 friends be seated round 2 tables if  [#permalink]

Show Tags

14 Sep 2014, 08:37
Ashishmathew01081987 wrote:
alphonsa wrote:
In how many ways can a group of 15 friends be seated round 2 tables if one of the tables can seat 10 and the other can seat 5 people?

A) 15C5 * 9! *4!
B) 15C3 * 8! *3!
C) 15C4 * 9! *3!
D) 15C2 * 10! *3!
E) 16C5 * 10! *4!

Source: 4gmat

IMO ans is A

Explanation

10 people can be selected from 15 people in 15C10 ways.
Remaining 5 people can be selected from 5 people in 5C5 ways.

Now, arranging 10 people on a round table = (10-1) ! = 9!
Arranging 5 people on a round table = (5-1) ! = 4!

Hence, total number of ways = 15C10 * 9! * 5C5 * 4!
= 15C5 * 9! * 4!

15C10

In general the simple formula for arranging 'n' things or persons around a circular table can be summarized as follows

1) Number of ways of arranging 'n' people on a circular table = (n-1) !
2) When clockwise or anticlockwise observation are not different then number of circular arrangements of 'n' different people = (n-1)! / 2

3) Number of selection of 'k' consecutive things out of 'n' things in a circle
= n when k<n
=1 when k = n
Intern
Joined: 30 Dec 2018
Posts: 4
Re: In how many ways can a group of 15 friends be seated round 2 tables if  [#permalink]

Show Tags

19 Sep 2019, 07:56
Couldn’t understand why did we do 15C10*5C5

Posted from my mobile device
Re: In how many ways can a group of 15 friends be seated round 2 tables if   [#permalink] 19 Sep 2019, 07:56
Display posts from previous: Sort by

In how many ways can a group of 15 friends be seated round 2 tables if

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

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