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In how many ways can 12 different books be distributed equally among 4

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In how many ways can 12 different books be distributed equally among 4  [#permalink]

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New post 24 Nov 2018, 09:03
4
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

24% (00:59) correct 76% (00:44) wrong based on 33 sessions

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GMATbuster's Weekly Quant Quiz#10 Ques #2


For Questions from earlier quizzes: Click Here


In how many ways can 12 different books be distributed equally among 4 different boxes?

A) 12C3
B) 12C4
C) 12C3*9C3*6C3
D) 12C4*8C4
E) 12C3*9C3*6C3*4!

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Re: In how many ways can 12 different books be distributed equally among 4  [#permalink]

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New post 24 Nov 2018, 09:15
1
Books have to be divided equally. So each box should get 12/4 = 3 books only.
So 1st box gets 3 books from 12 in 12C3 ways. Now, 9 books remaining.
So 2nd box gets 3 books from 9 in 9C3 ways. Now 6 books remaining.
So 3rd box gets 3 books from 6 in 6C3 ways. Now 3 books remaining.
So 4th box gets 3 books from 3 left in 3C3 ways or 1 way.

Ways of distributing 12 books among 4 similar boxes will be 12C3*9C3*6C3*1
Assuming that different boxes means which books go into which box will make a difference, then we will be able to arrange the total ways of distributing 12 books in 4! ways.

So total ways = 12C3*9C3*6C3*1*4!

Option E
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Re: In how many ways can 12 different books be distributed equally among 4  [#permalink]

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New post 24 Nov 2018, 09:27
E.
12 different books are there...and we have to divide in 4 boxes. So each group will have 3 books.

So number of ways for selecting 3 books is 12C3*9C3*6C3.

also since the 4 boxes are different we can arrange the group's among them.
So for that number of ways will be four.


So option E

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Re: In how many ways can 12 different books be distributed equally among 4  [#permalink]

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New post 24 Nov 2018, 09:30
Person 1:
3 books out of 12= 12C3
Person 2:
3 books out of 9= 9C3
Person 3:
3 books out of 6= 6C3
Person 4:
3 books out of 3= 3C3

Thus total possible solutions:
12C3x9C3x6C3x3C3x4!

4! is used because the 4 people can be arranged in 4! ways.

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Re: In how many ways can 12 different books be distributed equally among 4  [#permalink]

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New post 24 Nov 2018, 10:08
[quote="gmatbusters"]

GMATbuster's Weekly Quant Quiz#10 Ques #2


For Questions from earlier quizzes: Click Here


In how many ways can 12 different books be distributed equally among 4 different boxes?

A) 12C3
B) 12C4
C) 12C3*9C3*6C3
D) 12C4*8C4
E) 12C3*9C3*6C3*4!

12 different books be distributed equally among 4 different boxed in 12C3*9C3*6C3 ways
Ways to arrange these books in 4 different boxes is 4!
So the answer is 12C3*9C3*6C3*4!


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Re: In how many ways can 12 different books be distributed equally among 4  [#permalink]

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New post 24 Nov 2018, 13:54
For distributing 12 books equally across 4 boxes, we need to split 3 books in each.

First 3 books can be selected in 12C3 ways, second 3 is 9C3 ways, third 3 in 6C3 ways and last 3 in 3C3 ways.

Now, let four boxes be A, B, C and D. First box can be selected in 4 ways as it can be any of A, B, C or D. Lets say A is selected as first box. Similarly, Second box can be selected in 3 ways as it can be any from B, C and D and third box can be selected in 2 ways and last box in 1 way.

So, total number of ways = 12C3*9C3*6C3*3C3*4*3*2*1 = 12C3*9C3*6C3*1*4!

Hence, E is correct answer.
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Re: In how many ways can 12 different books be distributed equally among 4 &nbs [#permalink] 24 Nov 2018, 13:54
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