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 & Quail, and in order to serve on the HOA Governing Board, you must own a home in one of the two communities. There are 16 Eagle homeowners and 13 Quail homeowners that are interested in being on the HOA board.

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

b) How many ways are there to choose the five member board if there must be exactly 3 Eagle homeowners on the board?

c) What is the probability that a randomly chosen five member board would have exactly 3 Eagle homeowners on it?

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?

Explanation / Answer

Ans:

Number of eagle homeoners=16

Number of quail homeowners=13

a)Total homeowners=16+13=29

Number of ways 5 member board to be selected=29C5=(29*28*27*26*25)/(5*4*3*2*1)=118755

b)Number of ways choosing board having exactly 3 eagle homeowners=16C3*13C2

                                                                                                           =(16*15*14)/(3*2*1)*(13*12)/(2*1)

                                                                                =560*78

                                                                               =43680

c)Probability that a randomly chosen five member board would have exactly 3 eagle homeowners=(16C3*13C2)/29C5

=43680/118755

=0.3678

d)Number of ways to assign president and vice president for the board after choosing 5 member board=5P2=5*4=20

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.