A committee of 6 members is formed from a group of 7 gentlemen and 4 ladies. What is the probability that the committee includes at least 2 ladies?

Total ways = C(11,6) = 462. P(at least 2 ladies) = 1 − P(0 ladies) − P(1 lady). P(0 ladies) = C(7,6)·C(4,0)/462 = 7/462. P(1 lady) = C(7,5)·C(4,1)/462 = 21·4/462 = 84/462. So P(at least 2 ladies) = 1 − 7/462 − 84/462 = 1 − 91/462 = 371/462 = 53/66.