Math CentralQuandaries & Queries


Question from Mason, a student:

How many different 6 digit numbers can you make using the digits 1 ,2 5, 6, 7, and 9? How many of these six-digit numbers are divisible by 6?

Hi Mason,

I expect that you are to use each digit exactly once. The number of 6 digit numbers you can make from the digits 1, 2, 5, 6, 7 and 9 with each digit used only once is the number of permutations of 6 items taken 6 at a time.

An integer is divisible by 6 is and only if it is divisible by both 2 and 3. An integer is divisible by 2 if and only if its units digit is divisible by 2. In your list of digits only 2 and 6 are divisible by 2. How many in your list of 6 digit numbers have a 2 as the units digit? How many have a 6? For divisibility by 3 look at my response to Ben.



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