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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 k is?
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Number of ways to arrange boys and girls in a queue
To find the number of ways to arrange 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, we need to consider the possible arrangements.
Conditions for the arrangement
- The number of boys = 5
- The number of girls = 5
- In front of each girl, the number of girls is more than or equal to the number of boys
Determining the value of k
To calculate the value of k, we need to consider the girls as a single entity. So, the number of ways to arrange the 5 girls and 5 boys together is 10!.
Now, we need to consider the cases where the number of girls in front of a girl is more than or equal to the number of boys. This can be done in the following ways:
- 1 girl in front of a girl: This can be done in 5! ways
- 2 girls in front of a girl: This can be done in 4! ways
- 3 girls in front of a girl: This can be done in 3! ways
- 4 girls in front of a girl: This can be done in 2! ways
- 5 girls in front of a girl: This can be done in 1 way
Therefore, the total number of ways to arrange the boys and girls in the required manner is given by:
k = 10! - (5! + 4! + 3! + 2! + 1)
Calculating the value of k will give us the final answer.
To find the number of ways to arrange 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, we need to consider the possible arrangements.
Conditions for the arrangement
- The number of boys = 5
- The number of girls = 5
- In front of each girl, the number of girls is more than or equal to the number of boys
Determining the value of k
To calculate the value of k, we need to consider the girls as a single entity. So, the number of ways to arrange the 5 girls and 5 boys together is 10!.
Now, we need to consider the cases where the number of girls in front of a girl is more than or equal to the number of boys. This can be done in the following ways:
- 1 girl in front of a girl: This can be done in 5! ways
- 2 girls in front of a girl: This can be done in 4! ways
- 3 girls in front of a girl: This can be done in 3! ways
- 4 girls in front of a girl: This can be done in 2! ways
- 5 girls in front of a girl: This can be done in 1 way
Therefore, the total number of ways to arrange the boys and girls in the required manner is given by:
k = 10! - (5! + 4! + 3! + 2! + 1)
Calculating the value of k will give us the final answer.
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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 k is?
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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 k is? 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 k is? 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 k is?.
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 k is? 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 k is? 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 k is?.
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