Question

Answer the questions below.

(a) A certain committee consists of 15 people. From the committee, a president, a vice-president, a secretary, and a treasurer are to be chosen. In how many ways can these 4 offices be filled? Assume that a committee member can hold at most one of these offices. (b) A company has 38 salespeople. A board member at the company asks for a list of the top 5 salespeople, ranked in order of effectiveness. How many such rankings are possible?

Answer 1

a)

To select 4 positions in office out of 15 members, we can use the combination.

Number of ways of selecting 4 out of 15 members = 15C4 =

=15!(4!(15−4)!)

= 1365

b)

Firstly, to select 5 top members out of 38, we will use combination.

Number of ways of selecting 5 top members out of 38 = 38C5 =

=38!(5!(38−5)!)

= 501942

Now, those 5 can be arranged/re-arranged in 5! ways.

Total number = 501942 * 5! = 501942 * 120 = 60233040