Question

How many 7 digit phone numbers (using digit 0 to 9)can be formed if I can't be the first digit

Answer 1

It depends if the number can start with zero and if digits can repeat.

If digits can repeat and it can start with zero than there are 10 options for every digit so the answer is 10**7, or 10000000.

If it can’t start with zero but numbers can repeat, than there are 9 options for the first number and 10 for every other number. So 9 * 10**6, or 9000000.

If it can start with zero but no numbers can repeat than each digit has one less options than the one before it because one number has been used. so 10 * 9 * 8 * 7 * 6 * 5 * 4, or 604800.

If numbers can’t be repeated ant the first digit can’t be zero than the first 2 digits have 9 options, the first is anything but zero the second is zero plus the remaining 8 digits that aren’t zero that haven’t been used so 9 * 9 * 8 * 7 * 6 * 5 * 4, or 544320.