Math CentralQuandaries & Queries


Question from Christofer, a student:

What are all the possible 8 digit combinations of 0-9? List please. I know that there are 43046721 combinations but I want to know what they are.


We don't usually create such big long lists. However, I don't understand where you get 43046721 from.

The number of "possible 8 digit combinations of 0-9" is mathematically the number of unique sets of 8 numbers are selected from a group of 10 and order doesn't matter. This is expressed 10C8 and since this is the same number as choosing 2 numbers to be excluded, it is just 10 times 9 divided by 2. That makes 45 choices.

Perhaps you meant the number of possible 8 digit combinations of 0-9 where order does matter. You still can't re-use digits though. We call these permutations. This is expressed 10P8 and is just 10 times 9: 90 choices.

Or perhaps you meant the number of 8 digit numbers (repetitions permitted) using the digits 0-9. In that case, each digit has 10 choices and there are 8 of them, so the answer is 108 = 100 000 000.

When you use the word "combinations" it means something specific mathematically. I'm not sure what you really meant or how you arrived at the 43046721 figure, but I'm pretty sure it isn't combinations you are looking for if you think this number is close.

In any event, I suggest you write a quick little program on your computer to list what you want listed.

Stephen La Rocque.>

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