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

Answer:

(D) 70

Step-by-step 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.

$5C3=\frac{5!}{3!(5-3)!}$

$5C3=\frac{5*4*3*2!}{3*2*1*2!}$

$5C3=\frac{5*2*3}{3}$

$5C3=10$

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

$7C1=\frac{7!}{1!(7-1)!}$

$7C1=\frac{7*6!}{1*6!}$

$7C1=7$

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.