Question

In how many ways can five non-negative integers be added such that their sum does not exceed ten?

Answer 1

The possible ways are as follows:

Here we want to find 5 non-negative integers such that their sum is 10 or less than 10.

6,1,1,1,1   

5,1,1,1,1

5,2,1,1,1

4,1,1,1,1

4,1,1,1,2

4,1,1,1,3

4,1,1,2,2

3,1,1,1,1

3,1,1,1,2

3,1,1,1,3

3,1,1,2,2

3,1,1,2,3

3,1,2,2,2

2,1,1,1,1

2,1,1,1,2

2,2,2,1,1

2,2,2,2,1

2,2,2,2,2

1,1,1,1,1

Therefore total possible ways = 19