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In how many ways can 12 different books be distributed equal

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by BTGmoderatorDC » Thu Sep 05, 2019 5:37 pm
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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!

OA C

Source: e-GMAT
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by Jay@ManhattanReview » Thu Sep 05, 2019 8:28 pm
BTGmoderatorDC wrote: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!

OA C

Source: e-GMAT
Given there are 12 books to be distributed equally among 4 boxes, each box would have 3 books.

Number of ways of choosing 3 books out of 12 books for the first box = 12C3;
Number of ways of choosing 3 books out of the remaining 9 books for the second box = 9C3;
Number of ways of choosing 3 books out of the remaining 6 books for the third box = 6C3;
Number of ways of choosing 3 books out of the remaining 3 books for the fourth box = 3C3 = 1

Total number of ways = 12C3*9C3*6C3*1

The correct answer: C

Hope this helps!

-Jay
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