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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