Multiple choice

A1, A2, …….., A9 are nine friends who have to stand in three numbered rows such that only three of them stand in a row. In how many ways can they stand if A1, A2 and A3 should stand together in one row?

  1. 6!

  2. 2 × 6!

  3. 3 × 3! × 6!

  4. 6 × 6!

  5. 7!
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A1, A2, A3 must be in one row (3! ways to arrange them in that row). There are 3 rows to choose from. The remaining 6 friends can be arranged in the remaining 2 rows and the remaining spots in the first row in 6! ways. Total = 3 * 3! * 6!.

AI explanation

The group of three friends can be assigned to any of the three rows in 3 ways, and they can be arranged among themselves within that row in 3 factorial ways. Treating this group as a single unit along with the remaining six friends gives a total of seven units to arrange in the three rows, which can be done by placing the remaining six individuals in the other two rows in 6 factorial ways. Multiplying these independent choices gives 3 * 3! * 6!.

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