What is the coefficients of x^8 y^9 in the expansion of (3x + 2y)^17?
correct. to be more specific. the formula for binomial expansion is:
$\displaystyle (a + b)^n = \sum_{k = 0}^{n} {n \choose k}a^k b^{n - k}$
though i much prefer it in the order (it's exactly the same thing) of $\displaystyle \sum_{k = 0}^{n} {n \choose k}a^{n - k}b^k$
Here you have $\displaystyle a = 3x$ and $\displaystyle b = 2y$, and you want the term given by $\displaystyle k = 9$ (using the second formula)