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.

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.