A small combination lock on a suitcase has 5 wheels, each labeled with the 10 digits 0 to 9. How many 5 digit combinations are possible if no digit is repeated? If digits can be repeated? If successive digits must be different?

Here's the logic behind the answer.

There are eight possibilities for the first digit.

No matter what the first digit is, there are now only seven possibilities for the second digit, because you can't use the same digit again.

For the third digit there are 6 possibilities, because you've already used 2 digits and they can't repeat.

For the fourth, there are 5 possibilities.

For the fifth, there are 4 possibilities.

So, that gives you:
8 x 7 x 6 x 5 x 4 possibilities
or 6720 possibilities

A small combination lock on a suitcase has 5 ​wheels, each labeled with the 10 digits 0 to 9. How many 5 digit combinations are possible if no digit is​ repeated? If digits can be​ repeated? If successive digits must be​ different?

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A small combination lock on a suitcase has 5 wheels, each labeled with the 10 digits 0 to 9. How many 5 digit combinations are possible if no digit is repeated? If digits can be repeated? If successive digits must be different?