Question

Number of ways the sum of two can equal to another number

Answer 1

This problem is equivalent to finding the number of integer solutions to a+b+c+d+e=10a+b+c+d+e=10.

If you imagine your 1010 as a line of 1010stars then you can insert 44 "+" signs in between the stars to get a solution, for example +⋆⋆+⋆⋆⋆⋆+⋆+⋆⋆⋆+⋆⋆+⋆⋆⋆⋆+⋆+⋆⋆⋆represent the solution 0+2+4+1+30+2+4+1+3.