The student body of Ohio University has determined that an e

The student body of Ohio University has determined that an election will be held to replace the 5 Seniors that have graduated from the student officers.

15 males have submitted petitions for consideration as well as 20 females.

Evaluate the following combinations and compute the possibilities as required.

How many possible combinations are there regardless of who fills the positions?

How many possible combinations are there if 2 positions are filled by males?

How many possible combinations are there if 3 positions are filled by females?

If we choose 2 males and 3 females to fill the positions, how many combinations are there?

What is the probability of choosing 2 males and 3 females to fill these positions?

Solution

How many possible combinations are there regardless of who fills the positions?

15+20 = 35

35C5 = 324632

How many possible combinations are there if 2 positions are filled by males?

15C2 * 33C3 = 572880

How many possible combinations are there if 3 positions are filled by females?

20C3 * 32C2 = 565440

If we choose 2 males and 3 females to fill the positions, how many combinations are there?

15C2 * 20C3 = 119700

What is the probability of choosing 2 males and 3 females to fill these positions?

119700 / 324632 = 0.3687