Question:
In how many ways can 5 boys and 4 girls be seated in a row such that no two girls sit together?
5 लड़कों और 4 लड़कियों को एक पंक्ति में कितने प्रकार से बैठाया जा सकता है ताकि कोई भी दो लड़कियां एक साथ न बैठें?
Options:
- 43,200
- 28,800
- 14,400
- 57,600
- 43,200
- 28,800
- 14,400
- 57,600
Correct Answer: a)
Explanation:
First seat the 5 boys in a row: \(5! = 120\) ways.
This creates 6 available gaps (including ends): _ B1 _ B2 _ B3 _ B4 _ B5 _
The 4 girls must be seated in these 6 gaps: \(P(6, 4) = 6 \times 5 \times 4 \times 3 = 360\) ways.
Total arrangements = \(120 \times 360 = 43,200\).
This creates 6 available gaps (including ends): _ B1 _ B2 _ B3 _ B4 _ B5 _
The 4 girls must be seated in these 6 gaps: \(P(6, 4) = 6 \times 5 \times 4 \times 3 = 360\) ways.
Total arrangements = \(120 \times 360 = 43,200\).
5 लड़कों को बैठाने के तरीके = \(5! = 120\)। 6 खाली स्थानों में 4 लड़कियों को बैठाने के तरीके = \(P(6, 4) = 360\)। कुल तरीके = \(120 \times 360 = 43,200\)।