Multiple choice

In how many ways $9$ mathematics papers can be arranged, so that the best and the worst paper are always together

  1. $8!2!$
  2. $7!2!$
  3. $8!3!$

  4. None of these
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A Correct answer
Explanation

Treat the best and worst papers as a single unit. There are now 8 units to arrange (7 other papers + 1 pair), which can be done in 8! ways. The two papers within the unit can be arranged in 2! ways. Total ways = 8! * 2!.

AI explanation

Treat the best and worst papers as a single combined unit. This reduces the 9 individual papers into 8 units to arrange (the combined unit plus the remaining 7 papers). The number of ways to arrange these 8 units is 8!. The two papers within the combined unit can be arranged among themselves in 2! ways. Multiplying these gives 8! times 2!.

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