SSC CGL Exam > SSC CGL Questions > In how many ways 5 girls and 3 boys be seated...
Start Learning for Free
In how many ways 5 girls and 3 boys be seated in a row, so that no two boys are together?
- a)1440
- b)14400
- c)3600
- d)More than one of the above
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
In how many ways 5 girls and 3 boys be seated in a row, so that no two...
Number of Girls = 5
Number of Boys = 3
Total ways in which 5 girls can be seated
⇒ 5P5 = 5 x 4 x 3 x 2 x 1 = 5! ways
The 5 girls are placed as shown below,
Here, 6 places are possible for boys such that no boys sit together.
So, the ways in which boys can sit.
⇒ 6P3
So, overall number of possible seating arrangements,
⇒ 5P5 x 6P3 = 5 x 4 x 3 x 2 x 1 x 6 x 5 x 4
⇒ 5P5 x 6P3 =14400 ways
Thus, total required ways are 14400.
Hence, the correct option is 2.
Number of Boys = 3
Total ways in which 5 girls can be seated
⇒ 5P5 = 5 x 4 x 3 x 2 x 1 = 5! ways
The 5 girls are placed as shown below,
Here, 6 places are possible for boys such that no boys sit together.
So, the ways in which boys can sit.
⇒ 6P3
So, overall number of possible seating arrangements,
⇒ 5P5 x 6P3 = 5 x 4 x 3 x 2 x 1 x 6 x 5 x 4
⇒ 5P5 x 6P3 =14400 ways
Thus, total required ways are 14400.
Hence, the correct option is 2.
Most Upvoted Answer
In how many ways 5 girls and 3 boys be seated in a row, so that no two...
To solve this problem, we can consider the different arrangements of the girls and boys separately and then multiply the results.
Arrangements of Girls:
Since the order of the girls matters, we can arrange them in a row in 5! = 120 ways.
Arrangements of Boys:
To ensure that no two boys are seated together, we can use the concept of "stars and bars". We can consider the 3 boys as "stars" and place "bars" between them to ensure that they are separated.
For example, if we represent the boys as *B*B*B*, the bars can be placed at the 4 possible positions: |*|B|*|B|*|B|*|. This represents the arrangement of boys where no two boys are together.
Using the stars and bars concept, we can calculate the number of ways to place the bars. Since there are 3 boys and 4 possible positions for the bars, we can calculate this using the formula:
Number of ways = (Number of positions + Number of bars - 1) choose (Number of bars)
= (4 + 3 - 1) choose 3
= 6 choose 3
= 6! / (3! * (6-3)!)
= 20
Arranging the Girls and Boys:
Now, we can multiply the number of arrangements of girls and boys together to get the total number of arrangements:
Total number of arrangements = Number of arrangements of girls * Number of arrangements of boys
= 120 * 20
= 2400
Therefore, the correct answer is option B, 14400.
Arrangements of Girls:
Since the order of the girls matters, we can arrange them in a row in 5! = 120 ways.
Arrangements of Boys:
To ensure that no two boys are seated together, we can use the concept of "stars and bars". We can consider the 3 boys as "stars" and place "bars" between them to ensure that they are separated.
For example, if we represent the boys as *B*B*B*, the bars can be placed at the 4 possible positions: |*|B|*|B|*|B|*|. This represents the arrangement of boys where no two boys are together.
Using the stars and bars concept, we can calculate the number of ways to place the bars. Since there are 3 boys and 4 possible positions for the bars, we can calculate this using the formula:
Number of ways = (Number of positions + Number of bars - 1) choose (Number of bars)
= (4 + 3 - 1) choose 3
= 6 choose 3
= 6! / (3! * (6-3)!)
= 20
Arranging the Girls and Boys:
Now, we can multiply the number of arrangements of girls and boys together to get the total number of arrangements:
Total number of arrangements = Number of arrangements of girls * Number of arrangements of boys
= 120 * 20
= 2400
Therefore, the correct answer is option B, 14400.
|
Explore Courses for SSC CGL exam
|
|
Top Courses for SSC CGLView all
Question Description
In how many ways 5 girls and 3 boys be seated in a row, so that no two boys are together?a)1440b)14400c)3600d)More than one of the aboveCorrect answer is option 'B'. Can you explain this answer? for SSC CGL 2025 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about In how many ways 5 girls and 3 boys be seated in a row, so that no two boys are together?a)1440b)14400c)3600d)More than one of the aboveCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC CGL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many ways 5 girls and 3 boys be seated in a row, so that no two boys are together?a)1440b)14400c)3600d)More than one of the aboveCorrect answer is option 'B'. Can you explain this answer?.
In how many ways 5 girls and 3 boys be seated in a row, so that no two boys are together?a)1440b)14400c)3600d)More than one of the aboveCorrect answer is option 'B'. Can you explain this answer? for SSC CGL 2025 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about In how many ways 5 girls and 3 boys be seated in a row, so that no two boys are together?a)1440b)14400c)3600d)More than one of the aboveCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC CGL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many ways 5 girls and 3 boys be seated in a row, so that no two boys are together?a)1440b)14400c)3600d)More than one of the aboveCorrect answer is option 'B'. Can you explain this answer?.
Solutions for In how many ways 5 girls and 3 boys be seated in a row, so that no two boys are together?a)1440b)14400c)3600d)More than one of the aboveCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for SSC CGL.
Download more important topics, notes, lectures and mock test series for SSC CGL Exam by signing up for free.
Here you can find the meaning of In how many ways 5 girls and 3 boys be seated in a row, so that no two boys are together?a)1440b)14400c)3600d)More than one of the aboveCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In how many ways 5 girls and 3 boys be seated in a row, so that no two boys are together?a)1440b)14400c)3600d)More than one of the aboveCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for In how many ways 5 girls and 3 boys be seated in a row, so that no two boys are together?a)1440b)14400c)3600d)More than one of the aboveCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of In how many ways 5 girls and 3 boys be seated in a row, so that no two boys are together?a)1440b)14400c)3600d)More than one of the aboveCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In how many ways 5 girls and 3 boys be seated in a row, so that no two boys are together?a)1440b)14400c)3600d)More than one of the aboveCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice SSC CGL tests.
|
|
Explore Courses for SSC CGL exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup