Question

1) Answer each of the following problems. SHOW ALL NECESSARY WORK to fully justify each of your answers.

1. a) From a box of 24 tiny dolls, A toddler selects a set of 6 dolls as her favorites . How many different ways can she make this selection?

2. b) In how many different ways can the eleven players of a football team line up to be in a photograph

3. c) A store has to hire two cashiers. Five people are interviewed for the jobs. How many different ways can the hiring decisions be made?

4. d) Suppose that your English teacher asks you to choose 2 out of 6 books to read. How many different ways could you choose?

5. e) In how many ways can the three call letters of a radio station be arranged if the first letter must be a W or K, and no letters repeat?

Answer 1

(a)

Number of ways of selecting 6 dolls from 24 dolls is:

So,

Answer is:

134596

(b)

Number of ways of arranging 11 players = 11! =11 X 10 X 9 X 8 X 7 X 6 X 5 X 4 X 3 X 2 X 1 = 39916800

So,

Answer is:

39916800

(c)

Number of ways of selecting 2 cashiers from 5 people is:

So,

Answer is:

10

(d)

Number of ways of selecting 2 books from 6 books is:

So,

Answer is:

15

(e)

First letter can selected in 2 ways (W or K)

Second letter can selected in remaining 25 ways

Third letter can selected in remaining 24 ways

So,

Total number of ways = 2 X 25 X 24 = 1200

Answer is:

1200