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

Answer:

$165,20,\frac{4}{33}$

Step-by-step 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

$=11C_{3}=\frac{11!}{8!3!}$

$=165$

b)

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

$=6C_{3}=\frac{6}{3!3!}$

$=20$

c)

Probability that the selected group will consist of all women

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

$=\frac{6C_3}{11C_3}$

$=\frac{20}{165}=\frac{4}{33}$