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Question

The number of positive integral solutions of x+y+z=n is _____ .

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Solution

Direct formula
no. of positive integral solution of
x1+x2+......+x2=n
=n+z1Cr1
here r=3
n+31C31
n+2C2
(n+2)!n!2!=(n+2)(n+1)(n!)n!2
(n+1)(n+2)2

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