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

Total number of member is 16.

a. Ans: The number of ways which we can select a president, vice president and two secretaries (i.e., 4 board members) from 16 member is 16C4=1820.

b. Ans:

Total number of members who served longer than 10 year =16 - 12=4.

Therfore, the number of choices that a president and vice president that have served longer than 10 years is

4C2 =6.

c.Ans:

The number of member that have served less than 10 years is 12. Therefore, the number of choices of a president a vice president and two secretaries will consist entirely of board members that have served less than 10 years is

12C4=495.

d. Ans:

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)?

12C4/16C4 =495/1820=0.27198.

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