Upgrade subject to access all content

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?

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

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

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

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