How many arrangements of the numbers 1,2,3,4,5,6,7,8,9 are there where the sum of any two adjacent numbers is odd?

Guest Sep 10, 2021

#1**+1 **

For two adjacent numbers to have a odd sum, one of the numbers must be odd and the other must be even.

So, the numbers must be arranged as: O - E - O - E - O - E - O - E - O

There are 5 choices for the first odd number.

There are 4 choices for the first even number.

There are 4 choices for the second odd number.

There are 3 choices for the second even number.

There are 3 choices for the third odd number.

There are 2 choices for the third even number.

There are 2 choices for the fourth odd number.

There is 1 choice for the fourth (and last) even number.

There is 1 choice for the fifth (and last) odd number.

Multiplying these choices together: 5 x 4 x 4 x 3 x 3 x 2 x 2 x 1 x 1 choices.

geno3141 Sep 10, 2021