How many different 5 -letter radio station call letters can be made a. if the first letter must be Upper C comma Upper X comma Upper T comma or Upper M and no letter may be repeated? b. if repeats are allowed (but the first letter is Upper C comma Upper X comma Upper T comma or Upper M ) ? c. How many of the 5 -letter radio station call letters (starting with Upper C comma Upper X comma Upper T comma or Upper M ) have no repeats and end with the letter Upper S ?

a) 1,518,000

b) 2,284,880

c) 60,720

Step-by-step explanation:

a) a. if the first letter must be Upper C comma Upper X comma Upper T comma or Upper M and no letter may be repeated?

We draw 5 boxes, and based on that we will see the total possible cases. There are 26 alphabets

The first box should have C or X or T or M. No letter may be repeated.

Any Any Any Any Any

5 alphabets of the of the of the of the

C, X, T, M remaining remaining remaining remaining

25 alphabets 24 alphabets 23 alphabets 22 alphabets

Therefore; total possible call letters = 5 * 25 * 24 * 23 * 22 = 1,518,000

b)

The first box should have C or X or T or M Repeats as allowed

Any Any Any Any Any

5 alphabets of the of the of the of the

C, X, T, M remaining remaining remaining remaining

26 alphabets 26 alphabets 26 alphabets 26 alphabets

Therefore Total possible call letters = 5 * 26 * 26 * 26 * 26 = 2,284,880

c) The first box should have C, X, T, M and end with S

So the last place if fixed, and we now have 25 alphabets. The first box can go in 5 ways. The next box then will have only 24 letters to choose from, as the first box has taken a letter and the last box already has S in it. Repetition not allowed

Any Any Any Any S

5 alphabets of the of the of the is fixed

C, X, T, M remaining remaining remaining here

24 alphabets 23 alphabets 22 alphabets

Therefore Total possible call letters = 5 * 24 * 23 * 22 * 1 = 60,720