Multiple choice

In how many ways can 12 examination papers be arranged so that the best and the worst papers never comes together?

  1. $12! \times 11! \times 2!$
  2. $12! \times 10! \times 2!$
  3. $10 \times 11!$
  4. $9 \times 10!$
  5. $11 \times 12!$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total arrangements of 12 papers is 12!. If best and worst are together, treat them as one unit (11! ways to arrange) × 2! ways to order the two within the unit. Subtract from total: 12! - 11!×2! = 11!(12-2) = 10×11!.

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