Question

Suppose that we wish to expand (x+y+z)^17. What is the coefficient of x^2y^5z^10?

Answer 1

Use the extension of the binomial theorem: http://en.wikipedia.org/wiki/Multinomial_theorem

Answer 2

The coefficient is given by
\[\begin{pmatrix}17\\2,5,10\end{pmatrix}=\frac{17!}{(2!)(5!)(10!)}\]