Multiple choice

In how many ways can $8$ Indians, $4$ Americans and $4$ Englishmen can be seated in a row so that all the persons of same nationality sit together?

  1. $3!4!8!4!$
  2. $3!8!$
  3. $4!^2$
  4. $8!4!4!$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Treat each nationality group as a single unit. There are 3 groups, which can be arranged in 3! ways. Within each group, the individuals can be arranged in 8!, 4!, and 4! ways respectively. The total number of ways is 3! * 8! * 4! * 4!.

AI explanation

Treat each nationality group as a single block, giving 3 blocks that can be arranged in 3 factorial ways. The 8 Indians can be arranged within their block in 8 factorial ways, the 4 Americans in 4 factorial ways, and the 4 Englishmen in 4 factorial ways. Multiplying these independent arrangements gives the total arrangements as 3! 4! 8! 4!.

Keep practicing — related questions