In how many ways can 4 prizes be distributed among 5 students, if no student gets all the prizes?

Explanation

To solve the problem of distributing 4 prizes among 5 students such that no student receives all the prizes, we can follow these steps:

### Step-by-Step Solution:

1. **Calculate Total Distributions Without Restrictions:**
Each prize can be given to any of the 5 students. Therefore, for each of the 4 prizes, there are 5 choices.
\[
\text{Total ways} = 5^4 = 625
...