How many integer solutions to $x_1 + x_2 + x_3 + x_4 = 17$ are there if...
a) $x_i \ge -1$
b) $-1 \le x_i \le 5$
My solution for a) is $\binom{24}{21}$ and for b) it is $\binom{24}{21} - \binom{4}{1} \binom{17}{14} +\binom{4}{2} \binom{10}{7} - \binom{4}{3} \binom{3}{0} =20$
Just wondering if I've done these correctly as I can't find any solutions to cases where the integers can be negative as well on this site or in my text.