Question

A country has a 7 digit phone number system of the form ABC-DEFG. The first digit 'A' can be any number except O or 1. The next 2 digits , B' and 'C, can be any digit , except they cannot repeat . The last 4 digits can be any single digit number 0-9 . How many unique phone numbers are possible?

Answer 1

7,200,000

Explanation:

Number of Possibilities for

A) First Digit

There are 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) of which 0 and 1 is not allowed.

Hence there are 8 possibilities for the first digit

B) Second digit

There are 10 posibilities

C) Third digit

Since it mustn't be the same as Second digit....

There are 9 possibilities

D) Forth digit

There are 10 possibilities

E) Fifth digit

There are 10 possibilities

F) Sixth digit

There are 10 possibilities

E) Seventh digit

There are 10 possbilities

Total possible ways for the 7-digit phone number is...

8×10×9×10×10×10×10

=7,200,000 possible phone numbers