Multiple choice

In how many ways can $13$ question papers be arranged so that the best and the worst are never come together?

  1. $12!\times11$
  2. $11\times12!$
  3. $12!^2$

  4. none of these
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A Correct answer
AI explanation

The total number of ways to arrange 13 question papers is 13 factorial. To ensure the best and worst papers are never together, we treat them as a single unit, leaving 12 units to arrange in 12 factorial ways, and these two specific papers can be arranged within their unit in 2 factorial ways, giving 2 multiplied by 12 factorial arrangements where they are together. Subtracting this from the total gives 13 factorial minus 2 multiplied by 12 factorial, which simplifies by factoring out 12 factorial to 12 factorial multiplied by 11.

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