Permutation

[MBA.Aspirant]

In how many ways can 16 different gifts be divided among four children such that each child receives exactly four gifts?


A) 16^4
B) 4!^4
C) 16!/ 4!^4
D) 16!/ 4!
E) 4^16

[Frankenstein]

Hi,
Out of the 16, 4gifts are given to first guy in 16C4 ways
Out of the remaining 12, 4 can be given to 2nd guy in 12C4 ways
Out of the remaining 8, 4 can be given to 3nd guy in 8C4 ways
So, total number of ways is 16C4*12C4*8C4 = (16!/12!4!)(12!/8!4!)(8!/4!4!) = 16!/(4!)^4.

Hence, C

[amit2k9]

16c4 * 12c4 * 8c4 it is.