Question

A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?

A. 42
B. 70
C. 140
D. 165
E. 315

Answer 1

The total number of ways are 315.

Explanation:

Consider the provided information.

A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department.

Therefore the number of ways are:

`^7C_1 = 7` ways

There are 7 ways to fill math position.

2 of 10 candidates eligible to fill 2 identical positions in the computer science department.

Therefore the total number of ways are:

`^(10)C_2 = (10!)/(2!8!) = 45`

Hence, there are 45 ways to fill computer science position.

Total number of ways = 7 × 45 = 315 ways.

Hence, the total number of ways are 315.