Question

the number of triplets (x,y,z) which satisfy x+y+z = 15 where x,y,z are whole numbers is

Answer 1

136

Answer 2

This is a stars and bars problem. We want to find the number of non-negative integer solutions to $x+y+z = 15$. The formula is $\binom{n+k-1}{k-1}$, where $n=15$ and $k=3$. So, the number of solutions is $\binom{15+3-1}{3-1} = \binom{17}{2} = \frac{17 \times 16}{2} = 136$.