Question

A group consists of 6 men and 5 women. Four people are selected to attend a conference. In how many ways can 4 people be selected from this group of​ 11? In how many ways can 4 men be selected from the 6​ men? Find the probability that the selected group will consist of all men.

Answer 1

Answer:

A group consists of 6 men and 5 women.

Four people are selected to attend a conference.

Part A:

11C4 =$\frac{11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1}{4\times3\times2\times1\times7\times6\times5\times4\times3\times2\times1}$

= $\frac{11\times10\times9\times8}{4\times3\times2}$

= 330

Part B:

6C4 =

$\frac{6\times5\times4\times3\times2\times1}{4\times3\times2\times1\times2\times1}$

= 15

Part C:

$\frac{6C4}{11C4}$

The probability that the selected group will consist of all men is $\frac{15}{330} =\frac{1}{22}$