In how many ways can 4 prizes be distributed among 5 students, when No student gets more than one prize? A student may get any number of prizes? No student gets all the prizes?

Explanation

To solve the problem of distributing 4 prizes among 5 students under the given conditions, we can break it down into three parts as outlined in the question.

### Part 1: No student gets more than one prize

1. **Select 4 students from 5**: Since no student can get more than one prize, we first need to choose 4 students out of the 5 available. This can be done using the combination formula:
\[ \text{Number of ways to choose 4 students from 5} = \binom{5}{4} = 5 \]
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