Acertain 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

The total number of ways are 315.

Step-by-step 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:

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:

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.

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis: