In how many ways can you write the number 4 as the sum of 5 nonnegative integars?

Answer 1

Leaving aside permutations, there are five distict ways of writing the number 4 as the sum of 5 non-negative integers.

1. 0 + 0 + 0 + 0 + 4
2. 0 + 0 + 0 + 1 + 3
3. 0 + 0 + 0 + 2 + 2
4. 0 + 0 + 1 + 1 + 2
5. 0 + 1 + 1 + 1 + 1