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In how many ways can 5 boys and 5 girls be seated at a round table so that no two girls may be together ?
- a)4!
- b)5!
- c)4! + 5!
- d)4! × 5!
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
In how many ways can 5 boys and 5 girls be seated at a round table so ...
Leaving one seat vacant between two boys, 5 boys may be seated in 4! ways. Then at remaining 5 seats, 5 girls any sit in 5! ways.
Hence the required number = 4! × 5!
Hence the required number = 4! × 5!
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Community Answer
In how many ways can 5 boys and 5 girls be seated at a round table so ...
To solve this problem, we can fix the position of one of the girls on the table, and then arrange the remaining 4 girls and 5 boys around the table.
First, we fix the position of one of the girls. There are 5 possibilities for this. Let's label the girls as G1, G2, G3, G4, G5.
Next, we arrange the remaining 4 girls and 5 boys around the table. The 4 girls can be arranged in 4! ways, and the 5 boys can be arranged in 5! ways.
Therefore, the total number of ways to seat the 5 boys and 5 girls at a round table so that no two girls may be together is 5 * 4! * 5! = 5! * 4!.
The answer is therefore (d) 4!
First, we fix the position of one of the girls. There are 5 possibilities for this. Let's label the girls as G1, G2, G3, G4, G5.
Next, we arrange the remaining 4 girls and 5 boys around the table. The 4 girls can be arranged in 4! ways, and the 5 boys can be arranged in 5! ways.
Therefore, the total number of ways to seat the 5 boys and 5 girls at a round table so that no two girls may be together is 5 * 4! * 5! = 5! * 4!.
The answer is therefore (d) 4!
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In how many ways can 5 boys and 5 girls be seated at a round table so that no two girls may be together ?a)4!b)5!c)4! + 5!d)4! × 5!Correct answer is option 'D'. Can you explain this answer?
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