How many Positive integer solutions does the equation $x + y + z + w = 15$ have? How many Positive integer solutions does the equation $x + y + z + w = 15$ have?
Attempt:
Let $x = m + 1, y = n + 1, z = o + 1, w = p + 1 $
Then, $ m + 1 +  n + 1 + o + 1 +  p + 1 = 15$
$ m + n + o + p = 11 $

Hint:
Find the coefficient of $x^{15}$ of the following function: 
$$f(x)=(x+x^2+x^3+\cdots+x^{15})^4$$
Why this gives you the number of integer solution of your equation?
