...what is the probability that two women and a man will give presentations on the second day?

Question

A graduate class in computer science consists of six students, three men, and three women. During the last two days of the semester, presentations are made by the students, three presentations on each day. The professor randomly selects the students to make presentations. If, on the first of the two days, a man is selected to give the first presentation, what is the probability that two women and a man will give presentations on the second day?

Answer 1

As there are an equal number of men and women, P(2 women and a man give presentations on the second day) = P(2 men and a woman give presentations on the first day)

We are given that a man makes the first presentation on day 1. Thus, we are trying to find that, of the 3 women and 2 men remaining, 1 man and 1 woman make the next 2 presentations.

C(3,1)*C(2,1)/C(5,2) = 3*2/10 = 3/5