In how many ways can 5 examination papers be arranged so that the best and the worst papers never come together?

Question: In how many ways can 5 examination papers be arranged so that the best and the worst papers never come together?

Solution:
Total ways = 5!
= 120 ways

if two papers come together, we can consider them one.
ways that they will come together = 4! × 2!
= 24 × 2
= 48 ways

∴ ways the best and the worst papers never come together = 120 - 48 ways
= 72 ways