How many different telephone numbers are there if it is assumed that each number contains not more than seven digits (the first digit is not allowed to be 0 or 1 in a telephone number )?

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Solution

Well the first digit is not allowed to be 0 or 1 so 8 (2 to 9) remain to choose.

For the remaining 6 numbers you can make any choice from 000000 to 999999 when you count them these are $10^{6}$ (1 million) possibilities and when you consider the 8 possibilities you have for the first number there are $8 \times 10^{6}$ (8 million) possibilities total.

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