Question

How many different 6-letter radio station call letters can be made
a. if the first letter must be E, W, or T and no letter may be repeated?
b. if repeats are allowed (but the first letter is E, W, or T)?
c. How many of the 6-letter radio station call letters (starting with E, W, or T) have no repeats and end with the letter H?

a. If the first letter must be E, W, or T, and all the letters in the radio station call letters must be different, then there are _________ 6-letter radio station call letters.

b. If the first letter must be E, W, or T, and letters can be repeated, then there are __________ radio station call letters.

c. If the first letter must be E, W or T, and the last letter must be H and all the letters in the radio station call letters must be different, then there are ________ 6-letter words.

Answer 1

a) Given that the first letter must be E, W, or T and no letter may be repeated, the total number of 6-letter radio station call letters that can be made is computed here as

= Number of ways to select one of the three letters * Number of permutation of remaining 25 letters taken 5 at a time

Therefore there are 41400 possible call letters here.

b) Given that the repetition is allowed here, the total number of ways to make that here is computed as:

= Number of ways to select one of the three letters* Number of ways to select each of the 5 letters from 26 letters possible

= 3*26⁵ = 35644128

Therefore there are 35644128 possible call letters here.

c) Given that there are no repeats allowed, and the last letter is H, we have 3 ways to select the first letter and finally we are left with 24 letters to select the middle 4 letters. Therefore total ways to make here is computed as:

= 3*24*23*22*21

= 765072

Therefore there are 765072 possible call letters here.