Multiple choice

In how many ways can $10$ examination papers be arranged so that the best and worst papers are always together?

  1. $10!$
  2. $2\times9!$
  3. $9!$

  4. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Treat the best and worst papers as a single unit. There are 9 units to arrange (the pair + 8 others), which can be done in 9! ways. The pair can be arranged in 2! ways. Total = 2 * 9!.

AI explanation

Treat the best and worst papers as a single connected unit, which reduces the total number of units to arrange from 10 to 9. These 9 units can be arranged in 9! ways. The best and worst papers can be arranged among themselves in 2! = 2 ways, making the total number of arrangements 2 * 9!.

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