Math CentralQuandaries & Queries



using the numbers 0 thru 9 with combinations using each # no more than once what are the possible combinations using 1 thru 1234567890

Hi Mark.

Think about it this way. You have ten different balls each with a digit
written on it from 0 to 9. If you put them in a bag and draw them out
one by one and set them in positions A, B, C...J, how many different
possibilities are there?

For the first position A, you have ten balls to draw from, so there are
10 choices.

Now for the next position B, you have one less ball, so there are 9 choices.

If there were 10 choices for the first ball and 9 choices for the
second, then there are 10 x 9 = 90 possible permutations for "the first
two balls".

Now continue this pattern. How many choices for the next ball and so
on? Eventually you run out and the last position J must have the last
ball, so there is only 1 choice for that.

These are what we call "permutations". That's when order matters. When
order doesn't matter, we call them "combinations". Look up these words
on our Quick Search if you want more explanation and examples.

Steve La Rocque.

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