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 1: Calculate the total number of ways to distribute the prizes without any restrictions.
Each of the 4 prizes can be given to any of the 5 students. Therefore, the total number of ways to distribute the prizes is given by:
\[ 5 \times 5 \times 5 \times 5 = 5^4 = 625 \]

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