1.A board of trustees must select from its 16 members a president, vice presiden

Question

1.A board of trustees must select from its 16 members a president, vice president and two secretaries (both secretaries have same job).

a.How many different choices does the board of trustees have?

b.If there are 4 board members that have served longer than 10 years and 12 board members that have served less than or equal to 10 years how many of their choices will have a president and vice president that have served longer than 10 years?

c.How many of their choices of president vice president and two secretaries will consist entirely of board members that have served less than 10 years?

d.If one of these choices of president, vice president and two secretaries is chosen at random what is the probability that it will contain all junior board members (i.e. members with less than 10 years served)?

Explanation / Answer

a)no of different choices does the board of trustees= 16*15 *14C2 =21840

b)no of different choices does the board of trustees with President and Vice president have served longer than 10 years

=4* 3*14C2 =1092

c)no of their choices of president vice president and two secretaries will consist entirely of board members that have served less than 10 years = 12*11 *10C2 =5940

d)Probabilty=(12*11 *10C2 )/(16*15 *14C2 ) =5940/21840 =0.2719 =0.272

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