How many integer solutions are there to $x_1+x_2+x_3+x_4+x_5=31$


with
a) $x_igeq0$

b) $x_i>0$

c) $x_i geq i(i = 1, 2, 3, 4, 5)$

Now $a)$ seems simple enough to me, just use stars and bars to have $C(31+5-1, 31) = 52360$

But I’m completely stuck on b) and c), I’m not sure what do to with these constraints.

Any tips would be extremely appreciated.