Question

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

Answer 1

Answer:Case 1: no person gets more than 1 prize.  Same as (i), 5 ways  

Case 2: 1 person gets 2 prizes, 2 other people get 1 prize each.

Choose the person to get 2 prizes 5 ways.

Step-by-step explanation:a person may get any number of prizes.

The cases are the ways to split 4 prizes,

1. 1+1+1+1

2. 2+1+1

3. 2+2

4. 3+1

5. 4