Question

A small college with 1,200 total students has a student government of 40 members. From its members, the student government will elect a president, vice president, secretary, and treasurer. No single member can hold more than 1 of these 4 positions.

The permutation formula n Pr can be used to find the number of unique ways the student government can arrange its members into these positions,
What are the appropriate values of n and r?

Answer 1

Answer: N=40

r=4

Explanation:

We use the notation

�

P

�

nPrn, start text, P, end text, r to describe permutations. This notation represents the number of unique arrangements that exist when we select

�

rr objects without replacement from a set of

�

nn distinct objects.

In this scenario, how many students are we selecting to fill positions? How many students are we selecting from?

Hint #22 / 3

The student government is electing

4

44 of its

40

4040 members to fill the positions of president, vice president, secretary, and treasurer. So

�

nn should be

40

4040 and

�

rr should be

4

44.

Hint #33 / 3

These are the appropriate values of

�

nn and

�

rr:

�

=

40

�

=

4

n

r

​

=40

=4

​

Answer 2

20 New professors

Explanation:The current ratio is 1200%2F80 = 15.

The new ratio/proportion should be %281500%29%2Fx = 15.

From here, find x = 1500%2F15 = 100 professors.

They must hire 100-80 = 20 new professors.