Question

How many solutions are there to the inequality x1+x2+x3+x4≤15, where x1,x2,x3, and x4 are nonnegative integers?
Hint: Introduce an extra variable x5 and consider x1+x2+x3+x4+x5 = 15.

Answer 1

$N=C^{15}_{5+15-1}=C^{15}_{19}=\frac{19!}{15!4!}=3876$