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?

7,200,000

Step-by-step 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

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b