Multiple choice

In how many ways can 8 persons stand in a row, if one refuses to stand at the extreme end?

  1. 6 × 7!

  2. 6 × 8!

  3. 7 × 8!

  4. 7 × 7!

  5. 8!
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A Correct answer
Explanation

Total ways to arrange 8 persons = 8!. Ways where the specific person is at an end = 2 * 7!. Total ways - restricted ways = 8! - 2 * 7! = 8 * 7! - 2 * 7! = 6 * 7!.

AI explanation

From the 8 persons, 1 refuses to stand at either extreme end, so there are 6 allowable positions for this specific person. The remaining 7 persons can stand in any of the remaining 7 spots in 7! ways. The total number of arrangements is therefore 6 multiplied by 7!.

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