JEE Exam > JEE Questions > Please help me find what I did wrong: Q: A c...
Start Learning for Free
Please help me find what I did wrong: Q: A class is composed of 2 brothers and 6 other boys. How many ways can all the boys be seated so that 2 bros are not seated besides each others? My approach is: num of ways all 8 can seat - num of ways bros seat together. num of ways all the 8 boys can seat = 8! num of ways the 2 bros will seat together: [xx]234567 - taking the 2 bros as a single group [xx] num of ways bros seat together = 7!*2! Subtracting, I get 30240; but the correct answer is 3600?
Most Upvoted Answer
Please help me find what I did wrong: Q: A class is composed of 2 bro...
Understanding the Problem
To solve the problem of seating the boys such that the two brothers do not sit next to each other, we can use complementary counting. Your approach is mostly correct, but there’s a small miscalculation in the arrangement of the boys.
Calculating Total Arrangements
- The total number of ways to seat all 8 boys is:
8! = 40320
Calculating Arrangements with Brothers Together
- When considering the two brothers as a single unit, we treat them as one "block." Thus, we have:
- 1 block (the brothers) + 6 other boys = 7 units to arrange
- The number of arrangements for these 7 units is:
7! = 5040
- Within their block, the two brothers can switch places, which adds an additional factor of:
2! = 2
- Therefore, the number of ways for the brothers to sit together is:
7! × 2! = 5040 × 2 = 10080
Final Calculation for Brothers Not Together
- Now, to find the arrangements where the brothers are not sitting next to each other, subtract the arrangements where they are together from the total arrangements:
8! - (7! × 2!) = 40320 - 10080 = 30240
Correcting the Misunderstanding
The initial misunderstanding lies in the interpretation of the final answer. You calculated the arrangements correctly but missed that the question states the number of valid arrangements where the brothers are not seated together. The answer of 3600 might be from a different interpretation or error in calculation.
Thus, the correct outcome based on your approach is indeed:
30240 ways for the brothers not to sit together.
To solve the problem of seating the boys such that the two brothers do not sit next to each other, we can use complementary counting. Your approach is mostly correct, but there’s a small miscalculation in the arrangement of the boys.
Calculating Total Arrangements
- The total number of ways to seat all 8 boys is:
8! = 40320
Calculating Arrangements with Brothers Together
- When considering the two brothers as a single unit, we treat them as one "block." Thus, we have:
- 1 block (the brothers) + 6 other boys = 7 units to arrange
- The number of arrangements for these 7 units is:
7! = 5040
- Within their block, the two brothers can switch places, which adds an additional factor of:
2! = 2
- Therefore, the number of ways for the brothers to sit together is:
7! × 2! = 5040 × 2 = 10080
Final Calculation for Brothers Not Together
- Now, to find the arrangements where the brothers are not sitting next to each other, subtract the arrangements where they are together from the total arrangements:
8! - (7! × 2!) = 40320 - 10080 = 30240
Correcting the Misunderstanding
The initial misunderstanding lies in the interpretation of the final answer. You calculated the arrangements correctly but missed that the question states the number of valid arrangements where the brothers are not seated together. The answer of 3600 might be from a different interpretation or error in calculation.
Thus, the correct outcome based on your approach is indeed:
30240 ways for the brothers not to sit together.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
Please help me find what I did wrong: Q: A class is composed of 2 brothers and 6 other boys. How many ways can all the boys be seated so that 2 bros are not seated besides each others? My approach is: num of ways all 8 can seat - num of ways bros seat together. num of ways all the 8 boys can seat = 8! num of ways the 2 bros will seat together: [xx]234567 - taking the 2 bros as a single group [xx] num of ways bros seat together = 7!*2! Subtracting, I get 30240; but the correct answer is 3600?
Question Description
Please help me find what I did wrong: Q: A class is composed of 2 brothers and 6 other boys. How many ways can all the boys be seated so that 2 bros are not seated besides each others? My approach is: num of ways all 8 can seat - num of ways bros seat together. num of ways all the 8 boys can seat = 8! num of ways the 2 bros will seat together: [xx]234567 - taking the 2 bros as a single group [xx] num of ways bros seat together = 7!*2! Subtracting, I get 30240; but the correct answer is 3600? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Please help me find what I did wrong: Q: A class is composed of 2 brothers and 6 other boys. How many ways can all the boys be seated so that 2 bros are not seated besides each others? My approach is: num of ways all 8 can seat - num of ways bros seat together. num of ways all the 8 boys can seat = 8! num of ways the 2 bros will seat together: [xx]234567 - taking the 2 bros as a single group [xx] num of ways bros seat together = 7!*2! Subtracting, I get 30240; but the correct answer is 3600? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Please help me find what I did wrong: Q: A class is composed of 2 brothers and 6 other boys. How many ways can all the boys be seated so that 2 bros are not seated besides each others? My approach is: num of ways all 8 can seat - num of ways bros seat together. num of ways all the 8 boys can seat = 8! num of ways the 2 bros will seat together: [xx]234567 - taking the 2 bros as a single group [xx] num of ways bros seat together = 7!*2! Subtracting, I get 30240; but the correct answer is 3600?.
Please help me find what I did wrong: Q: A class is composed of 2 brothers and 6 other boys. How many ways can all the boys be seated so that 2 bros are not seated besides each others? My approach is: num of ways all 8 can seat - num of ways bros seat together. num of ways all the 8 boys can seat = 8! num of ways the 2 bros will seat together: [xx]234567 - taking the 2 bros as a single group [xx] num of ways bros seat together = 7!*2! Subtracting, I get 30240; but the correct answer is 3600? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Please help me find what I did wrong: Q: A class is composed of 2 brothers and 6 other boys. How many ways can all the boys be seated so that 2 bros are not seated besides each others? My approach is: num of ways all 8 can seat - num of ways bros seat together. num of ways all the 8 boys can seat = 8! num of ways the 2 bros will seat together: [xx]234567 - taking the 2 bros as a single group [xx] num of ways bros seat together = 7!*2! Subtracting, I get 30240; but the correct answer is 3600? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Please help me find what I did wrong: Q: A class is composed of 2 brothers and 6 other boys. How many ways can all the boys be seated so that 2 bros are not seated besides each others? My approach is: num of ways all 8 can seat - num of ways bros seat together. num of ways all the 8 boys can seat = 8! num of ways the 2 bros will seat together: [xx]234567 - taking the 2 bros as a single group [xx] num of ways bros seat together = 7!*2! Subtracting, I get 30240; but the correct answer is 3600?.
Solutions for Please help me find what I did wrong: Q: A class is composed of 2 brothers and 6 other boys. How many ways can all the boys be seated so that 2 bros are not seated besides each others? My approach is: num of ways all 8 can seat - num of ways bros seat together. num of ways all the 8 boys can seat = 8! num of ways the 2 bros will seat together: [xx]234567 - taking the 2 bros as a single group [xx] num of ways bros seat together = 7!*2! Subtracting, I get 30240; but the correct answer is 3600? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of Please help me find what I did wrong: Q: A class is composed of 2 brothers and 6 other boys. How many ways can all the boys be seated so that 2 bros are not seated besides each others? My approach is: num of ways all 8 can seat - num of ways bros seat together. num of ways all the 8 boys can seat = 8! num of ways the 2 bros will seat together: [xx]234567 - taking the 2 bros as a single group [xx] num of ways bros seat together = 7!*2! Subtracting, I get 30240; but the correct answer is 3600? defined & explained in the simplest way possible. Besides giving the explanation of
Please help me find what I did wrong: Q: A class is composed of 2 brothers and 6 other boys. How many ways can all the boys be seated so that 2 bros are not seated besides each others? My approach is: num of ways all 8 can seat - num of ways bros seat together. num of ways all the 8 boys can seat = 8! num of ways the 2 bros will seat together: [xx]234567 - taking the 2 bros as a single group [xx] num of ways bros seat together = 7!*2! Subtracting, I get 30240; but the correct answer is 3600?, a detailed solution for Please help me find what I did wrong: Q: A class is composed of 2 brothers and 6 other boys. How many ways can all the boys be seated so that 2 bros are not seated besides each others? My approach is: num of ways all 8 can seat - num of ways bros seat together. num of ways all the 8 boys can seat = 8! num of ways the 2 bros will seat together: [xx]234567 - taking the 2 bros as a single group [xx] num of ways bros seat together = 7!*2! Subtracting, I get 30240; but the correct answer is 3600? has been provided alongside types of Please help me find what I did wrong: Q: A class is composed of 2 brothers and 6 other boys. How many ways can all the boys be seated so that 2 bros are not seated besides each others? My approach is: num of ways all 8 can seat - num of ways bros seat together. num of ways all the 8 boys can seat = 8! num of ways the 2 bros will seat together: [xx]234567 - taking the 2 bros as a single group [xx] num of ways bros seat together = 7!*2! Subtracting, I get 30240; but the correct answer is 3600? theory, EduRev gives you an
ample number of questions to practice Please help me find what I did wrong: Q: A class is composed of 2 brothers and 6 other boys. How many ways can all the boys be seated so that 2 bros are not seated besides each others? My approach is: num of ways all 8 can seat - num of ways bros seat together. num of ways all the 8 boys can seat = 8! num of ways the 2 bros will seat together: [xx]234567 - taking the 2 bros as a single group [xx] num of ways bros seat together = 7!*2! Subtracting, I get 30240; but the correct answer is 3600? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE 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