What’s the probability that all 5 selected are women?

Question

An executive committee consists of 15 members: 7 men & 8 women. 5 members are selected at random to attend a meeting in Hawaii. The names are drawn from a hat.

Answer 1

n = 15 members (7 men and 8 women)

k = 5 members selected to attend a meeting in Hawaii

C(15, 5) = 15! / (5!)(10!) = 3003 ways to select 5 members to attend a meeting in Hawaii

C(8, 5) = 8! / (5!)(3!) = 56 ways to select 5 women to attend a meeting in Hawaii

P(5 members selected are women) = C(8, 5) / C(15, 5) = 56/3003 = 0.01865

The probability that all 5 members selected are women is 0.01865.

Answer 2

Will select five women out of 8 and 0 men out of 7 out of all the possible ways to select 5 out of 15.

C(8,5) * C(7,0)

------------------- where C(8,5) = 8!/(5!3!). Similarly for C(7,0) and C(15,5) = 0.0186

C(15,5)