SOLUTION: 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

Question 1038390: 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 14 Eagle homeowners and 11 Quail homeowners that are interested in being on the HOA board.

a) If the board is made up of 8 members, how many different ways are there to choose the board?

____________________ways to choose the board?

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

_____________ways to choose the eight member board with exactly 2 Eagle homeowners?

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

Probability that a eight member board has exactly 2 Eagle homeowners =
Round your answer to 4 decimal places as needed.

d) If the eight 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 eight member board?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
There are 14 Eagle homeowners and 11 Quail homeowners that are interested in being on the HOA board.
s) If the board is made up of 8 members, how many different ways are there to choose the board? :: 25C8 ways to choose the board?
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b) How many ways are there to choose the eight member board if there must be exactly 2 Eagle homeowners on the board?::
14C2 * 11C6 ways to choose the eight member board with exactly 2 Eagle homeowners?
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c) What is the probability that a randomly chosen eight member board would have exactly 2 Eagle homeowners on it?::[14C2*11C6]/25C8
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Round your answer to 4 decimal places as needed:: 0.0389
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d) If the eight board members have now been chosen, how many ways would there be to assign a President and Vice President for the board?:: 8P2 = 8*7 = 56
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Cheers,
Stan H.
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