Math CentralQuandaries & Queries


Question from Edward, a parent:

using the number 12345678 how many 7, 6,5,4,3 & 2 digit numbers can you make when not using any number twice in the same number

Hi Edward,

There are 8 possible 1 digit numbers you can make. Each one of them you can extend to a 2 digit number in 7 ways since you have 7 digits left to choose from. Thus there are 8 × 7 possible 2 digit numbers.

In the same way, each of the 2 digit numbers can be extended to a 3 digit number in 6 ways since there are 6 digits to choose from. Thus there are 8 × 7 × 6 possible 3 digit numbers.

Continue in the same way,

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