Multiple choice

In how many ways can 5 boys and 4 girls be arranged in a line so that there will be a boy at the beginning and at the end?

  1. 3! .7! /5!

  2. 5!.7!/6!

  3. 5!.7!/3!

  4. 3!.7!./5!

  5. 3!.7!/7!
Reveal answer Fill a bubble to check yourself
C Correct answer
AI explanation

To ensure a boy is at both ends, we select and arrange 2 boys for the first and last positions in 5P2 ways, which equals 5! / 3!. The remaining 7 individuals (3 boys and 4 girls) can be arranged in the middle 7 positions in 7! ways. Multiplying these together gives (5! / 3!) multiplied by 7!, or 5! . 7! / 3!. The result is 5!.7!/3!.

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