The Binomial theorem says that: (x + y)^n = sigma^n_k = 0 x^n - k y^k = (n 0) x^n y^0 + (n 1) x^n - 1 y^1 + (n 2)x^n - 2y^2 + ... + (n n)y^n a) Find the coefficient of x^2 y in the expansion of (x + y)^3 b) Expand (2x - 3y)^3 c) What is the coefficient of x^12 y^13 in the expansion of (2x - 3y)^25 A committee of size 7 is chosen from 6 men, 7 women and 8 children. What is the probability that the committee contains a) 2 men, 4 women, 1 child _____ b) 2 men