vaibhav101 wrote:in how many ways can 12 books be divided among 3 boys so that each receives 4 books?
A 36540
B 34560
C 34650
D 35640
E 36450
Take the task of distributing the 12 books and break it into
stages
Let's say the children are named A, B and C
Stage 1: Select 4 books to give to child A
Since the order in which we select the 4 books does not matter, we can use combinations.
We can select 4 books from 12 books in 12C4 ways (= 12!/(4!)(8!))
So, we can complete stage 1 in
12!/(4!)(8!) ways
Stage 2: select 4 books to give to child B
There are now 8 books remaining
We can select 4 books from 8 books in 8C4 ways (= 8!/(4!)(4!))
So, we can complete stage 2 in
8!/(4!)(4!) ways
Stage 4: select 4 books to give to child C
There are now 4 books remaining
NOTE: There's only 1 way to select 4 books from 4 books, but if we want this result to look like the others, let's do the following:
We can select 4 books from 4 books in 4C4 ways (= 4!/4!)
So, we can complete stage 3 in
4!/4! ways
By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus distribute all 12 books) in
[12!/(4!)(8!)][8!/(4!)(4!)][4!/4!] ways
A BUNCH of terms cancel out to give us 12!/(4!)³, which evaluates to be 34650
Answer: C
--------------------------
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video:
https://www.gmatprepnow.com/module/gmat-counting?id=775
Then you can try solving the following questions:
EASY
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https://www.beatthegmat.com/what-should ... 67256.html
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https://www.beatthegmat.com/counting-pr ... 44302.html
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https://www.beatthegmat.com/picking-a-5 ... 73110.html
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https://www.beatthegmat.com/permutation ... 57412.html
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https://www.beatthegmat.com/simple-one-t270061.html
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https://www.beatthegmat.com/mouse-pellets-t274303.html
MEDIUM
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https://www.beatthegmat.com/combinatori ... 73194.html
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https://www.beatthegmat.com/arabian-hor ... 50703.html
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https://www.beatthegmat.com/sub-sets-pr ... 73337.html
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https://www.beatthegmat.com/combinatori ... 73180.html
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https://www.beatthegmat.com/digits-numbers-t270127.html
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https://www.beatthegmat.com/doubt-on-se ... 71047.html
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https://www.beatthegmat.com/combinatori ... 67079.html
DIFFICULT
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https://www.beatthegmat.com/wonderful-p ... 71001.html
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https://www.beatthegmat.com/ps-counting-t273659.html
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https://www.beatthegmat.com/permutation ... 73915.html
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https://www.beatthegmat.com/please-solv ... 71499.html
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https://www.beatthegmat.com/no-two-ladi ... 75661.html
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https://www.beatthegmat.com/laniera-s-c ... 15764.html
Cheers,
Brent
