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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, and the first digit is 1?

 Jan 9, 2022
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Add digits:  1, 3, 5, 7, 9

Even digits:  2, 4, 6, 8

 

There is only 1 way to choose the first number.

Then, there are 4 ways to choose the even number.

Followed by 4 ways to choose the next odd number.

                     3 ways to choose the next even number

                     3 ways to choose the next odd number

                     2 ways to choose the nexteven number

                     2 ways to choose the next odd number

                     1 way to choose the last even number

                     1 way to choose the last odd number.

 

Multiplying these together:  1 x 4 x 4 x 3 x 3 x 2 x 2 x 1 x 1  =     ...  the answer.

 Jan 9, 2022

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