Integer Solutions to $x_1+x_2+\ldots+x_n$ = number

Question

The question is how many solutions to the equation $a+b+c+d+e+f+g=20$ are there if all terms are nonnegative integers and $a+b+c=10$?

To answer this, would I just take the number of solutions to $a+b+c=10$ and multiply it by the number of solutions to $d+e+f+g=10$?

Answer 1

This is basically correct. To figure out the number of solutions to $a+b+c=10$ and $d+e+f+g=10$, you can use the method of 'stars and bars'.