BTGmoderatorLU wrote: ↑

Sat Nov 14, 2020 11:44 am

Source: Magoosh

An office has 6 employees; there are 5 female employees and 1 male employee. In how many ways can a 3-person committee be created if the committee must include the male employee?

A. 10
B. 12
C. 15
D. 24
E. 30

The OA is A

In order to ensure that the 3-person committee includes the male employee, we'll start by placing the male employee on the committee.
Our task now is to choose 2 more people (from the 5 female employees) to join the male on the committee.

Since the order in which we select the two people does not matter, we can use combinations.
We can select 2 employees from 5 employees in 5C2 ways (= 10 ways)

Answer: A

Cheers,
Brent

BTGmoderatorLU wrote: ↑

Sat Nov 14, 2020 11:44 am

Source: Magoosh

An office has 6 employees; there are 5 female employees and 1 male employee. In how many ways can a 3-person committee be created if the committee must include the male employee?

A. 10
B. 12
C. 15
D. 24
E. 30

The OA is A

Solution:

Since the sole male employee must be chosen, the remaining 2 employees for the 3-person committee must be female. Since there are 5 female employees, the number of ways to choose 2 female employees from 5 is 5C2 = (5 x 4)/2 = 10.

Answer: A