I need help understanding the steps to take for each question please!

Question

The executives in a company are four women and three men. Three are to be chosen at random to attend a management seminar.

(a) If one of the executives is chosen at random to draw the names out of a hat, what is the probability that the person drawing the names is a woman?

(b) How many ways can the group of attendees be formed if there are no restrictions on composition?

(c) How many ways can one man be chosen?

(d) How many ways can 2 women be chosen?

(e) What is the probability that the random selection of the three-person group will result in two women and one man?

Answer 1

a) 4/7

b) C(7,3) - combinations of 7 taken 3 at a time = 7!/(4!3!)

c) C(3,1)

d) C(4,2)

e) C(4,2)*C(3,1)/C(7,3)