Question

A student club has 60 members. They want to elect two officers who will serve as the president and the vice president of the club. The club bylaws dictate that the selections be done without replacement and that the first person selected would serve as the president and the second person selected would serve as the vice president. Calculate how many different ways the selections can be made if: a) There is no restriction on who is elected and whoever is elected will accept to serve. (2 Points) b) Two members, say A and B, will accept to serve only if they are elected to serve together. (3 Points)

Answer 1

3540

2

Explanation:

Total number of members = 60

Number of members to be elected = 2

Since the order of selection matters as the first is president and second is vice president ;

Using the permutation formula :

nPr = n! ÷ (n-r)!

60P2 = 60! ÷ (60 - 2)!

60P2 = 60! ÷ 58!

60P2 = 3540

B.) 2 members A and B will accept to serve only if they are selected to serve together ;

Since only 2 members (president and vice president) are to be chosen ; Hence, only the tow of them (A and B) will be chosen, to do this ;

2P2 = 2! /(2 - 2)! = 2! / 0! = (2*1)/1 = 2