Kenneth Rosen Edition 7 Exercise 6.1 Question 7 (Page No. 396)

Question

How many different three-letter initials can people have?

Answer 1

There are 26 letters in the alphabet.

Using product rule:

       = 26 x 26 x 26 

       = 17576 different three-letter initials people can have.

Answer 2

Here tottal nos different letters are 26.

we have to choose three different letters.

so the job is consists of three segment.

first segment can be done in 26 ways , second segment of choosing different letter after choosing thr first one can be done in 25 ways  and similarly the third one can be done in 24 ways after choosing the first and second ones.

hence the total process can be done in 26*25*24=15600.

however if the repeat of the same letter is allowed then choosing of first,second and third can be done 26,26,26 ways and the total nos ways will ne=17576 ways.