How do I find the coefficient of a^2b^4 in the expansion of (a - b)^6?

Question

How do I find the coefficient of a^2b^4 in the expansion of (a - b)^6?

Answer 1

(x + y)^n = sum of (nCr) x^(n-r) y^r

if y is negative, they alternate in signs.. . . multiply by (-1)^r

thus you are needing

nCr ... where x = a , y = b, n = 6 , r = 4

thus

6C4 * (1)^6 = 6!/2!4! = 15