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How many nine-digit numbers can be made using each of the digits 1 through 9 exactly once with the digits alternating between odd and even?

 Jun 2, 2021
 #1
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If it starts with an even

There are 4 first digit possibilities (not 5 becasue it can's start with 0)  , 4 third digits 3 fifth digits etc  so that is    4*4!  *   (now for the odd digits)  4!

 

If it starts with an odd then there will be  5!*4! different ones

 

Now add them together.

 

4*4!*4! + 5!*4!

 Jun 2, 2021

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