Question

A cellphone/telephone keypad has keys numbered from 0 to 9 inclusive, and eight of these keys are also lettered. How many different telephone numbers are possible with this keypad, if each "number" consists of two letters followed by five numbers, where the first number is not zero?

Answer 1

5,760,000

Explanation:

A cellphone/telephone keypad has keys numbered from 0 to 9 inclusive, and eight of these keys are also lettered. How many different telephone numbers are possible with this keypad, if each "number" consists of two letters followed by five numbers, where the first number is not zero?

this can be solved using permutations

8 · 8 · 9 · 10 · 10 · 10 · 10 = 5,760,000

the above is the number of telephone numbers

Answer 2

There are:
8 · 8 · 9 · 10 · 10 · 10 · 10 = 5,760,000 different telephone numbers