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The number of ways of arranging 5 boys and 5 girls in a queue of infront of each girl number of girls are more than or equal to the number of boys is equal to k the value of kis?
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Arranging 5 Boys and 5 Girls in a Queue
To find the number of ways of arranging 5 boys and 5 girls in a queue where in front of each girl, the number of girls is more than or equal to the number of boys is equal to k.
Key Points:
- We have a total of 10 children (5 boys and 5 girls) to arrange in a queue.
- The condition given is that in front of each girl, the number of girls should be more than or equal to the number of boys.
Solution:
Step 1: Arrange the Girls
- Since the number of girls in front of each girl should be more than or equal to the number of boys, we first arrange the 5 girls in a queue.
- This can be done in 5! ways (5 factorial).
Step 2: Arrange the Boys
- Now, we need to place the boys in the queue. Since the number of girls in front of each girl should be more than or equal to the number of boys, the boys can only be placed in the remaining positions after the girls have been arranged.
- The boys can be arranged in the remaining 5 positions in 5! ways.
Step 3: Find the Total Number of Ways
- By the multiplication principle, the total number of ways of arranging 5 boys and 5 girls in a queue where in front of each girl, the number of girls is more than or equal to the number of boys is equal to k is:
- Total number of ways = 5! * 5! = 120 * 120 = 14400
Therefore, the value of k is 14400.
To find the number of ways of arranging 5 boys and 5 girls in a queue where in front of each girl, the number of girls is more than or equal to the number of boys is equal to k.
Key Points:
- We have a total of 10 children (5 boys and 5 girls) to arrange in a queue.
- The condition given is that in front of each girl, the number of girls should be more than or equal to the number of boys.
Solution:
Step 1: Arrange the Girls
- Since the number of girls in front of each girl should be more than or equal to the number of boys, we first arrange the 5 girls in a queue.
- This can be done in 5! ways (5 factorial).
Step 2: Arrange the Boys
- Now, we need to place the boys in the queue. Since the number of girls in front of each girl should be more than or equal to the number of boys, the boys can only be placed in the remaining positions after the girls have been arranged.
- The boys can be arranged in the remaining 5 positions in 5! ways.
Step 3: Find the Total Number of Ways
- By the multiplication principle, the total number of ways of arranging 5 boys and 5 girls in a queue where in front of each girl, the number of girls is more than or equal to the number of boys is equal to k is:
- Total number of ways = 5! * 5! = 120 * 120 = 14400
Therefore, the value of k is 14400.
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The number of ways of arranging 5 boys and 5 girls in a queue of infront of each girl number of girls are more than or equal to the number of boys is equal to k the value of kis?
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The number of ways of arranging 5 boys and 5 girls in a queue of infront of each girl number of girls are more than or equal to the number of boys is equal to k the value of kis? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The number of ways of arranging 5 boys and 5 girls in a queue of infront of each girl number of girls are more than or equal to the number of boys is equal to k the value of kis? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of ways of arranging 5 boys and 5 girls in a queue of infront of each girl number of girls are more than or equal to the number of boys is equal to k the value of kis?.
The number of ways of arranging 5 boys and 5 girls in a queue of infront of each girl number of girls are more than or equal to the number of boys is equal to k the value of kis? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The number of ways of arranging 5 boys and 5 girls in a queue of infront of each girl number of girls are more than or equal to the number of boys is equal to k the value of kis? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of ways of arranging 5 boys and 5 girls in a queue of infront of each girl number of girls are more than or equal to the number of boys is equal to k the value of kis?.
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