Exercise 1.a committee of five people is chosen randomly from four men and six women. find the probability that: a) exactly four women are on the committee: b) at least four women are on the committee: c) at most four women are on the committee:

Answer with explanation:

Given : Number of men = 4

Number of women = 6

Total people =

Total number of ways to make a committee of five people from 10 persons :-

a) Number of ways to make committee that has exactly four women :

The  probability that committee has exactly four women :

b) Number of ways to make committee that has at-least four women :

The probability that committee at-least four women :

c) Number of ways that committee has more than 4 women :-

The probability that committee has more than 4 women :-

Now, the  probability that committee has at most four women :-