How many solutions does the equation x + y + w + z = 15 have if x, y, w, z are all non-negative integers? Combinatorics question:
What I tried for solving this problem is (16 - 1 + 4 choose 4). I got 16 from the numbers 0 thought 16 as possible values for x, y , w or z. 
However apparently the answer is (16 - 1 + 3 choose 3). Can someone explain to me where this 3 is coming from since there are 4 variables , x y w z.

The way I remember it is to put the number of $+'s$ at the bottom,
and add it to the required total at top, hence simply $\dbinom{15+3}{3}$
And if the requirement is for positive integers, preplace $1's$ for each variable,
and apply the same formula, so $\dbinom{11+3}{3}$
