This is one form of stars and bars problem where x,y,z should be non zero.
The number of solutions to the equation x+y+z=17 where x,y,z are positive integers, is given by
(n−1 C k−1)
Here, n=17,k=3 and thus we will get 120 as answer.
Ref: https://en.wikipedia.org/wiki/Stars_and_bars_%28combinatorics%29
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