Question

In how many different ways can 8 players be arranged in a line so that the best and worst players are never together?

Answer 1

The number of permutations which has the best and worse students are 8P2=56.

Out of these permutations, there are 7*2 = 14 permutations which have the best and worst players next to each other. Therefore, the number of permutations where the best and worst players aren't together is 56-14=42.

The other six players can be arranged in 6! = 720 ordered ways.

Therefore, the total is 720*42 = 30,240 ordered ways.