Select the correct answerIn how many ways can 5 boys and 5 girls sit in a circle so that no two boys sit together?Options4!×4!5!×5! /24!×5!5!×5!
Question
Select the correct answer
In how many ways can 5 boys and 5 girls sit in a circle so that no two boys sit together?
Options:
- 4! × 4!
- 5! × 5! / 24!
- 5! × 5!
Solution
The correct answer is 5!×5!.
Here's the step-by-step solution:
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First, arrange the 5 boys in a circle. The number of ways to arrange n objects in a circle is (n-1)!. So, the number of ways to arrange 5 boys is (5-1)!= 4!= 24.
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Now, consider the spaces between the boys. There are 5 spaces between the boys where the girls can sit.
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Arrange the 5 girls in these 5 spaces. The number of ways to arrange 5 girls in 5 spaces is 5!= 120.
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Therefore, the total number of ways to arrange 5 boys and 5 girls in a circle so that no two boys sit together is 4!×5!= 24×120= 2880.
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