What is the coefficient of x8y9 in the expansion of 3x 2y17

What is the coefficient of x^8y^9 in the expansion of
(3x + 2y)^17?

Solution

General binomial formula is:

(a+b)^n = sum(k=0 to k=n)[(n,k)a^k*b^(n-k)], where

(n,k) = n!/(k!(n-k)!).

In your case a=3x, b=2y, n=17, and k=8. Therefore,
the term for k=8 is:

(17!/(8!9!))*(3x)^8*(2y)^9 = [(17!/(8!9!)*3^8*2^9]*x^8*y^9.