Multiple choice

In how many ways can 7 Indians, 5 Pakistanis and 6 Dutch be seated in a row so that all persons of the same nationality sit together?

  1. 3!

  2. 7!5!6!

  3. 3!.7!.5!.6!

  4. 182
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Treat each nationality group as a single block. There are 3! ways to arrange the 3 blocks, and within each block, the individuals can be arranged in 7!, 5!, and 6! ways respectively.

AI explanation

We treat each nationality as a single block, giving 3 blocks that can be arranged in 3! ways. The 7 Indians can be arranged among themselves in 7! ways, the 5 Pakistanis in 5! ways, and the 6 Dutch in 6! ways. The total number of seating arrangements is the product of these values, 3! times 7! times 5! times 6!.

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