Bunuel wrote:

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. \frac{(16!)}{(4!)^4}

D. \frac{(16!)}{(4!)}

E. 4^{16}

Kudos for correct solution.

Here,

16 gifts are distributed among 4 children such that each receives exactly 4 gifts can be arranged in = 16C4

Now, we are left with 12 gifts which can be arranged in = 12C4

Now, we are left with 8 gifts that can be arranged in = 8C4

then we are left with 4 gifts which can be arranged in= 4C4

Total no. of ways = 16C4 * 12C4 * 8C4 * 4C4

=

\frac{(16!)}{(4!)^4}
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