Question

A group consists of five men and six women. Three people are selected to attend a conference. a. In how many ways can three people be selected from this group of eleven ​? b. In how many ways can three women be selected from the six ​women? c. Find the probability that the selected group will consist of all women.\

Answer 1

`165,20,(4)/(33)`

Explanation:

GIVEN: A group consists of five men and six women. Three people are selected to attend a conference.

TO FIND: a) In how many ways can three people be selected from this group of eleven. ​b) In how many ways can three women be selected from the six ​women. c) Find the probability that the selected group will consist of all women.

SOLUTION:

a)

Total ways in which three people be selected from this group of eleven is

`=11C_(3)=(11!)/(8!3!)`

`=165`

b)

Total ways in which three women can be selected from the six ​women

`=6C_(3)=(6)/(3!3!)`

`=20`

c)

Probability that the selected group will consist of all women

`=\frac{\text{total ways in which three women can be selected}}{\text{total ways of selection}}`

`=(6C_3)/(11C_3)`

`=(20)/(165)=(4)/(33)`