Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 05 Jul 2015, 00:28

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# How many ways are there to split a group of 6 boys into two

Author Message
TAGS:
Intern
Joined: 13 Nov 2010
Posts: 24
Followers: 1

Kudos [?]: 4 [0], given: 0

How many ways are there to split a group of 6 boys into two [#permalink]  25 Nov 2010, 16:06
5
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

48% (01:29) correct 52% (00:41) wrong based on 105 sessions
How many ways are there to split a group of 6 boys into two groups of 3 boys each? (The order of the groups does not matter)

A. 8
B. 10
C. 16
D. 20
E. 24
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Jul 2013, 09:15, edited 1 time in total.
Edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 28272
Followers: 4476

Kudos [?]: 45231 [0], given: 6646

Re: ways to split a group of 6 boys into two groups of 3 boys ea [#permalink]  25 Nov 2010, 16:13
Expert's post
2
This post was
BOOKMARKED
yufenshi wrote:
How many ways are there to split a group of 6 boys into two groups of 3 boys each? (The order of the groups does not matter)

8
10
16
20
24

The official answer is B, but I don't understand why in this case we need to divide by 2. It seems to me to be the same questions as: how many ways to choose 3 people out of 6 people. in that case it would be 20.

Thanks!

GENERAL RULE:
1. The number of ways in which $$mn$$ different items can be divided equally into $$m$$ groups, each containing $$n$$ objects and the order of the groups is important is $$\frac{(mn)!}{(n!)^m}$$

2. The number of ways in which $$mn$$ different items can be divided equally into $$m$$ groups, each containing $$n$$ objects and the order of the groups is NOT important is $$\frac{(mn)!}{(n!)^m*m!}$$.

BACK TO THE ORIGINAL QUESTION:
In original question as the order is NOT important, we should use second formula, $$mn=6$$, $$m=2$$ groups $$n=3$$ objects (people):
$$\frac{(mn)!}{(n!)^m*m!}=\frac{6!}{(3!)^2*2!}=10$$.

This can be done in another way as well: $$\frac{C^3_6*C^3_3}{2!}=10$$, we are dividing by $$2!$$ as there are 2 groups and order doesn't matter.

For example if we choose with $$C^3_6$$ the group {ABC} then the group {DEF} is left and we have two groups {ABC} and {DEF} but then we could choose also {DEF}, so in this case second group would be {ABC}, so we would have the same two groups: {ABC} and {DEF}. So to get rid of such duplications we should divide $$C^3_6*C^3_3$$ by factorial of number of groups - 2!.

This concept is also discussed at:
combinations-problems-95344.html?hilit=dividing%20objects%20order#p734396
split-the-group-101813.html?hilit=split
9-people-and-combinatorics-101722.html?hilit=divided%20equally%20into#p788744
ways-to-divide-99053.html?hilit=divided%20equally%20into#p763471

Hope it helps.
_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 5682
Location: Pune, India
Followers: 1413

Kudos [?]: 7342 [0], given: 186

Re: ways to split a group of 6 boys into two groups of 3 boys ea [#permalink]  25 Nov 2010, 20:49
Expert's post
and after going through Bunuel's explanation, to ensure that you have understood the concept, try the question in this post: http://gmatclub.com/forum/combination-105384.html

It the same reason why you do not multiply by 2 in the question in this post.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Senior Manager Joined: 08 Nov 2010 Posts: 419 WE 1: Business Development Followers: 7 Kudos [?]: 54 [0], given: 161 Re: ways to split a group of 6 boys into two groups of 3 boys ea [#permalink] 27 Nov 2010, 12:24 if i used the 6!/3!*(6-3)! * 1/2 is that ok as well? _________________ Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 5682 Location: Pune, India Followers: 1413 Kudos [?]: 7342 [0], given: 186 Re: ways to split a group of 6 boys into two groups of 3 boys ea [#permalink] 27 Nov 2010, 12:44 Expert's post 144144 wrote: if i used the 6!/3!*(6-3)! * 1/2 is that ok as well? Absolutely! You are doing 6C3 * (1/2). _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Math Expert
Joined: 02 Sep 2009
Posts: 28272
Followers: 4476

Kudos [?]: 45231 [0], given: 6646

Re: ways to split a group of 6 boys into two groups of 3 boys ea [#permalink]  27 Nov 2010, 13:12
Expert's post
VeritasPrepKarishma wrote:
144144 wrote:
if i used the
6!/3!*(6-3)! * 1/2 is that ok as well?

Absolutely! You are doing 6C3 * (1/2).

I'd say it depends on the logic behind this formula.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 5373
Followers: 310

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

Re: How many ways are there to split a group of 6 boys into two [#permalink]  17 Aug 2014, 03:17
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: How many ways are there to split a group of 6 boys into two   [#permalink] 17 Aug 2014, 03:17
Similar topics Replies Last post
Similar
Topics:
1 In how many ways can be 6 boys and 6 girls sit around circular table 1 22 Jan 2015, 06:52
6 How many ways are there to split a group of 6 boys into two 16 06 Sep 2011, 08:35
3 If a choir consists of 5 boys and 6 girls, in how many ways can the 10 10 Oct 2007, 22:36
4 In how many ways to choose a group of 3 people from 6 couples so that 13 10 Aug 2006, 18:14
7 In how many ways 5 boys and 6 girls can be seated on 12 11 22 Jan 2006, 00:44
Display posts from previous: Sort by