2 questions..

Use inclusion-exclusion to find the number of solutions in non-negative integers to:

a) x1 + x2 + x3 + x4 = 56

With conditions

x1 <= 20

x2 >= 16

8 <= x3 <= 38

b) x1 + x2 + x3 + x4 + x5 = 73

x2 <= 30

5<= x3 <= 40

x4 >= 7

I'm having trouble with these harder questions which contain upper and lower bounds and not quite understanding the adding and subtracting of intersections :\

If you could help out it would be greatly appreciated. Thank you very much