a)
x1 +x2 + x3 + x4 = 32
x1 +x2 + ..xr = n
number of integral solution = (n+ r -1)C(r-1)
here n = 32 , r = 4
hence
(32 + 4 - 1)C(4-1)
= 35C3
= 35*34*33/6
= 6545
b)
x1 = 2 +y1 . x2 = 2 +y2 ,x3 = 1 + y3 , x4 = 1 +y4
hence
x1 +x2 + x3 + x4 = 32
2+y1 + 2 +y2 + 1 +y3 + 1 +y4 = 32 . yi >= 0
y1 +y2 +y3 +y4 = 26
= (29C3)
= (29*28*27/6)
= 3654
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