How many ways can the six members of a hockey team line up at the blue line so that the two defencemen are not side by side?
+130516 1 2 3 4 5 6
A 4 x 4! = 96
A 3 x 4! = 72
A 3 x 4! = 72
A 3 x 4! = 72
A 3 x 4! = 72
A 4 x 4! = 96
Look at the diagram above...assuming A and B were the defensemen....A could occupy the 1st position and B could occupy any of 4 other positions......the other players could be arranged in 4! ways..........so 4 x 4! = 96
And A could occupy the 2nd position, B could occupy any of 3 other positions, and the 4 other players could be arranged in 4! ways.....so 4 x 4! = 72
Etc.
So......
96(2) + 72(4) = 480 ways
