Consider I have the following rectangular array:

0 0 0 0

1 1 1 1

2 2 2 2

3 3 3 3

4 4 4 4....

Suppose I have to choose one number from each column. I then have to take the sum of the numbers and then divide it by 5 and take the remainder.

Prove that:

a.) the number of combinations that yield a remainder of 0, equals the number of of combinations that yield a remainder of 1, equals the number of combinations that yield a remainder of 2.... etc.