Math CentralQuandaries & Queries


Question from Hannah:

I have a briefcase with a three-digit code. I can set the code myself using digits 1 through 9, assuming that each digit can only be used once. How many possible codes are there?

Hi Hannah,

Stat by choosing the first digit. You have 9 choices. Each one digit code can extend each to a two digit code in 8 ways since you can't repeat the first digit. Hence you have $9 \times 8$ possible two digit codes. Each of these can be extended to a three digit code in 7 ways.


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