+1286 Find the number of ways of arranging the numbers 1,2 ,3, 4, 5, 6 in a row so that the product of any two adjacent numbers is at least 5.
+129895 Here's my attempt...
1 5 x x x x and the other numbers can be arranged in 4! ways
1 6 x x x x and the other numbers can be arranged in 4! ways
x x x x 5 1 and the other numbers can be arranged in 4! ways
x x x x 6 1 and the other numbers can be arranged in 4! ways
5 1 6 x x x ....the 5 1 6 can occupy any of 4 positions and the other numbers can be arranged in 3! ways
6 1 5 x x x ... the 6 1 5 can occupy any of 4 positions and the other numbers can be arranged in 3! ways
So
4 *4! + 2* 4*3! = 144 ways
