You have decided you may want to join your Home Owner\'s Association (HOA) Gover

Question

You have decided you may want to join your Home Owner's Association (HOA) Governing Board. Your HOA serves two adjoining communities called Eagle & and in order to serve on the HOA Governing Board, you must own a home in one of the two communities. There are 10 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 3 Eagle homeowners on the board? ways to choose the eight member board with exactly 3 Eagle homeowners. c) What is the probability that a randomly chosen eight member board would have exactly 3 Eagle homeowners on it? Probability that a eight member board has exactly 3 Eagle homeowners - 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.

Explanation / Answer

(c) probability for choosing exactly 3 eagle member from 10 eagle and 5 quail member from 11quail

P = (Ways to form a group for choosing exactly 3 eagle member from 10 eagle and 5 quail member from 11quail) / (ways to form a 8 member group out of 21 member)

P = 55440 / 203490 = 0.27244

(d) for choosin president from 8 member there are = 8 ways

and after that choosing vice president from 7 member there are = 7 ways

So total ways to chose president and vice preident = 8*7 = 56 ways

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