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

A group consists of 6 men and 5 women.

Four people are selected to attend a conference.

Part A:

11C4 =
`(11*10*9*8*7*6*5*4*3*2*1)/(4*3*2*1*7*6*5*4*3*2*1)`

=
`(11*10*9*8)/(4*3*2)`

= 330

Part B:

6C4 =

`(6*5*4*3*2*1)/(4*3*2*1*2*1)`

= 15

Part C:

`(6C4)/(11C4)`

The probability that the selected group will consist of all men is
`(15)/(330) =(1)/(22)`