Question Help In a club with 7 male and 11 female​ members, a 3 -member committee will be randomly chosen. Find the probability that the committee contains at least 2 women.

Question

Please try and figure out as fast as possible

Answer 1

The committee contains 3 women or 2 women and one man.

Consider a 3-woman committee first. The probability is (11/18)(10/17)(9/16)=55/272.

Now 1 man + 2 women: (7/18)(11/17)(10/16)=385/2448. But there are 3 ways of arranging the man and two women so this reduces to 385/816. Add together these probabilities=275/408=0.6740 or 67.4%.