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Kenneth Rosen Edition 7 Exercise 6.1 Question 9 (Page No. 396)

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three letters will be different but first letter will be A.

Hence the second letter can be choosen in 25 ways and similarly the third letter can be choosen in 24 ways.

Hence the ways of choosing three different letters will be 1*25*24=600 ways.
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26 Alphabets

1 letter = 1 way ( since it must be 'A')

2 letter = 26 ways

3 letter = 26 ways

Total ways = 1 x 26 x 26 

                 = 676 ways

676 different three-letter initials are there that begin with an A.

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Kenneth Rosen Edition 7 Exercise 6.1 Question 21 (Page No. 396)
How many positive integers between $50$ and $100$ are divisible by $7?$ Which integers are these? are divisible by $11?$ Which integers are these? are divisible by both $7$ and $11?$ Which integers are these?
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