Question

3) You have decided you may want to join your Home Owner's Association (HOA) Governing Board. Your HOA serves two adjoining communities called Eagle & Quail, and in order to serve on the HOA Governing Board, you must own a home in one of the two communities. There are 13 Eagle homeowners and 16 Quail homeowners that are interested in being on the HOA board.

a) If the board is made up of 5 members, how many different ways are there to choose the board?


ways to choose the board.
DO NOT TYPE COMMAS OR ANSWERS WILL BE MARKED INCORRECT.

b) How many ways are there to choose the five member board if there must be exactly 2 Eagle homeowners on the board?


ways to choose the five member board with exactly 2 Eagle homeowners.
DO NOT TYPE COMMAS OR ANSWERS WILL BE MARKED INCORRECT.

c) What is the probability that a randomly chosen five member board would have exactly 2 Eagle homeowners on it?


Probability that a five member board has exactly 2 Eagle homeowners =
DO NOT TYPE COMMAS OR ANSWERS WILL BE MARKED INCORRECT.
Round your answer to 4 decimal places as needed.

d) If the five board members have now been chosen, how many ways would there be to assign a President and Vice President for the board?


ways to choose a President and Vice President for the five member board.
DO NOT TYPE COMMAS OR ANSWERS WILL BE MARKED INCORRECT.

Answer 1

a) Number of different ways to form the committee of 5 members is computed here as:

= Number of ways to select 5 items from (13 + 16) = 29 items

b) Number of ways to choose the five member board if there must be exactly 2 Eagle homeowners on the board is computed here as:

= Number of ways to choose 2 Eagle homeowners * Number of ways to choose 3 Quail homeowners

c) Probability that a randomly chosen five member board would have exactly 2 Eagle homeowners on it is computed by using the answers to the previous 2 parts as:

= Number of ways to choose 2 Eagle homeowners * Number of ways to choose 3 Quail homeowners / Number of ways to select 5 items from (13 + 16) = 29 items

Therefore 0.3678 is the required probability here.

d) Given that the 5 board team is already selected number of ways to give the president and vice president post is computed here as:

= Number of ways to choose the president from 5 candidates * Number of ways to choose a vice president from the remaining 4 candidates

= 5*4 = 20

Therefore there are 20 ways to make the selection here.