Question

Of the 12 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 12 temporary employees are women, how many of the possible groups of 4 temporary employees consist of 3 women and 1 man?(A) 22

(B) 35
(C) 56
(D) 70
(E) 105

Answer 1

(D) 70

Explanation:

We have been given that 5 of the 12 temporary employees are women.

So the number of men will be
`12-5=7`.

We are asked to find the number of possible groups of 4 temporary employees that consist of 3 women and 1 man.

Since there are 5 women, so we can select 3 women from 5 women is
`5C3` ways.

`5C3=(5!)/(3!(5-3)!)`

`5C3=(5*4*3*2!)/(3*2*1*2!)`

`5C3=(5*2*3)/(3)`

`5C3=10`

Since there are 7 men, so we can select 1 man from 7 men is
`7C1` ways.

`7C1=(7!)/(1!(7-1)!)`

`7C1=(7*6!)/(1*6!)`

`7C1=7`

Total groups of 4 temporary employees consisting 3 women and 1 man would be
`10*7=70`

Therefore, there are 70 possible groups of 4 temporary employees consisting 3 women and 1 man.