$x_1, x_2, x_3, x_4, x_5, x_6$ are all nonnegative integers. Find the number of solutions to these equations:

a) $x_1+x_2+x_3=10$

b) $x_1+x_2+x_3+x_4+x_5+x_6=20$

(Hint: think of putting n balls into k distinguishable boxes.)