Math CentralQuandaries & Queries


Question from Sophie:

I have forgotten the order in what the numbers go for my padlock! The numbers are, 0125, they don't have any repeats like, 0001, 0002. What are all possible the combinations? Help!

Hi Sophie,

There are not that many so you can list them all. Reading from left to right there are 4 choices for the first digit, 0, 1, 2 or 5. Once you have chosen the first digit there are 3 choices for the second digit since you can't repeat the first. Thus there are $4 \times 3$ choices for the first two digits. Again, regardless of what two digits you have chosen there are 2 choices for the third digit and hence $4 \times 3 \times 2$ choices for the first three digits. Finally you have only one choice for the fourth digit so in total there are $4 \times 3 \times 2 \times 1 = 24$ possibilities.

But you want to list tem.

If the first two digits are 0 and 1 then the possibilities are

0125 and

If the first two digits are 0 and 2 then the possibilities are

0215 and

If the first two digits are 0 and 5 then the possibilities are

0512 and

Thus there are six possibilities if the first digit is 0.

What if the first digit is 1 or 2 or 5?


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