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Combinatorics

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Distributing Stars to Students, More than 3

COMBIN-XXYL5R

How many ways are there to distribute $k$ identical gold stars to $n$ Learnerator students so that no student gets more than three gold stars?

A

$$\sum_{i = 0}^n (-1)^i {n \choose i}{(k - 3i) + n - 1 \choose n-1}$$

B

$$\sum_{i = 0}^n (-1)^i {n \choose i}{(k - 3i) + n - 1 \choose n}$$

C

$$\sum_{i = 0}^n (-1)^i {n \choose i}{(k - 4i) + n - 1 \choose n-1}$$

D

$$\sum_{i = 0}^n (-1)^i {n \choose i}{(k - 4i) + n - 1 \choose n}$$