UPSC Exam > UPSC Questions > The number of ways of arranging 5 boys and 5 ...
Start Learning for Free
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 k, then k/(5!)^2 is?
Most Upvoted Answer
The number of ways of arranging 5 boys and 5 girls in a queue of infro...
Explanation:
Arranging the boys and girls:
- There are 5 boys and 5 girls to be arranged in a queue.
- The condition is that in front of each girl, the number of girls must be more than or equal to the number of boys.
Calculating the total number of ways (k):
- Let's first calculate the total number of ways to arrange the boys and girls without any restrictions.
- Total ways = 10! (arranging 10 people)
- Now, we need to subtract the number of ways where the condition is violated.
- If we fix a boy, there are 5! ways to arrange the boys and 5! ways to arrange the girls in front of him.
- So, the number of ways the condition is violated = 5! * 5!
- Therefore, the number of ways the condition is satisfied (k) = Total ways - Violating ways = 10! - 5! * 5!
Calculating k/(5!)^2:
- k = 10! - 5! * 5!
- k = 10! - 5! * 5!
- k = 10 * 9 * 8 * 7 * 6 * 5! - 5! * 5!
- k = 5! * (10 * 9 * 8 * 7 - 5)
- k = 5! * 3025
- k = 5! * 3025
- k/(5!)^2 = 3025
Therefore, k/(5!)^2 = 3025.
Arranging the boys and girls:
- There are 5 boys and 5 girls to be arranged in a queue.
- The condition is that in front of each girl, the number of girls must be more than or equal to the number of boys.
Calculating the total number of ways (k):
- Let's first calculate the total number of ways to arrange the boys and girls without any restrictions.
- Total ways = 10! (arranging 10 people)
- Now, we need to subtract the number of ways where the condition is violated.
- If we fix a boy, there are 5! ways to arrange the boys and 5! ways to arrange the girls in front of him.
- So, the number of ways the condition is violated = 5! * 5!
- Therefore, the number of ways the condition is satisfied (k) = Total ways - Violating ways = 10! - 5! * 5!
Calculating k/(5!)^2:
- k = 10! - 5! * 5!
- k = 10! - 5! * 5!
- k = 10 * 9 * 8 * 7 * 6 * 5! - 5! * 5!
- k = 5! * (10 * 9 * 8 * 7 - 5)
- k = 5! * 3025
- k = 5! * 3025
- k/(5!)^2 = 3025
Therefore, k/(5!)^2 = 3025.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Top Courses for UPSCView all
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 k, then k/(5!)^2 is?
Question Description
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 k, then k/(5!)^2 is? for UPSC 2024 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 k, then k/(5!)^2 is? covers all topics & solutions for UPSC 2024 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 k, then k/(5!)^2 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 k, then k/(5!)^2 is? for UPSC 2024 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 k, then k/(5!)^2 is? covers all topics & solutions for UPSC 2024 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 k, then k/(5!)^2 is?.
Solutions 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 k, then k/(5!)^2 is? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of 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 k, then k/(5!)^2 is? defined & explained in the simplest way possible. Besides giving the explanation of
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 k, then k/(5!)^2 is?, a detailed solution 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 k, then k/(5!)^2 is? has been provided alongside types of 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 k, then k/(5!)^2 is? theory, EduRev gives you an
ample number of questions to practice 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 k, then k/(5!)^2 is? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup