I got that the total number of telephone numbers: $10^{10}$, but should I do the number of one $0$ in prefix, number of two $0$ in prefix and number of three $0$ in prefix, and subtract them. But I don't know how to count the number of $0$ in the prefix.
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In the US, at least, 0 and 1 are not valid numbers for the first digit. – shade4159 Nov 05 '13 at 00:41
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If all numbers have $10$ digits, $3$ in the prefix and $7$ in the remainder, and your only limitation is that you can not have a $0$ in the prefix, you should have: $$9^3\cdot 10^7$$
Possibilities. If say, you could not have either of two digits in the prefix (i.e. a choice of $8$ digits, you would simply replace the $9$ by an $8$.
Nathaniel Bubis
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does it mean that if I change 0 in the problem to any other numbers, the answer will be the same? – SSS Nov 05 '13 at 00:42
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