What is the probability that all 4 selected are men​?

Question

executive committee consists of 12 ​members: 5 men and 7 women.

4 members are selected at random to attend a meeting in Hawaii. The names are drawn from a hat.

Answer 1

The probability that the first person drawn is a man is 5/12 because there are 5 men and 12 total names.

For the 2nd draw, the probability that the person drawn is a man is 4/11 because there are now 4 men and 11 total names (since the first one drawn was a man and is no longer in the pool to draw from).

For the 3rd draw, the probability that the person drawn is a man is 3/10 because there are now 3 men and 10 total names.

For the 4th draw, the probability that the person drawn is a man is 2/9 because there are now 2 men and 9 total names.

So the probability of ALL of those things happening is the product of the 4 so: 5/12•4/11•3/10•2/9 = (5•4•3•2)/(12•11•10•9) = 120/11880 = 1/99 (or 1.01%)