Question

You are staffing a new department, and you have applications on your desk. You will hire 2 of the 5 software engineers who have applied, and 3 of the 7 computer engineers who have applied. What is the total number of possible complete staffs you could hire

Answer 1

Answer:

The total number of possible complete staffs you could hire is 350.

Step-by-step explanation:

The order that the software engineers are is not important. For example, hiring John and Laura as the software engineers is the same as hiring Laura and John. The same applies for the computer engineers. So we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

What is the total number of possible complete staffs you could hire?

2 software engineers from a set of 5

3 computer engineers from a set of 7

So

$T = C_{5,2}*C_{7,3} = \frac{5!}{2!3!}*\frac{7!}{3!4!} = 10*35 = 350$

The total number of possible complete staffs you could hire is 350.