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Find the number of ways of arranging the numbers 1,2 ,3, 4, 5, 6, 7, 8, 9 in a row so that the product of any two adjacent numbers is even.

 May 29, 2023
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There are 5 odd digits: 1, 3, 5, 7, 9

There are 4 even digits: 2, 4, 6, 8

 

The arrangements must begin with an odd number and end in an odd number:

 

Therefore, there are: 5!  x  4! ==120  x  24 ==2,880 such even arrangements possible.

 May 29, 2023

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