Question

If the best and the worst papers never appear together, find in how many ways six examination papers can be arranged.

Answer 1

If the best and worst papers appear always together, the number of ways is $5!\times 2$. Therefore, the required number of ways is as follows.
Total number of ways without any restrictions$-$Number of ways when best and wort paper are together $=6!-5!\times 2=480$.