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Five children, Anaxagoras, Beatrice, Childeric, Desdemona, and Ethelred, sit randomly in five chairs in a row. What is the probability that Childeric and Ethelred sit next to each other?
- a)1/30
- b)1/15
- c)1/5
- d)2/5
- e)7/20
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Five children,Anaxagoras,Beatrice,Childeric,Desdemona, andEthelred, si...
First, we will count all the possible arrangements of the five children on the five seats, all the possible orders. This is 5! = 120. That’s the denominator.
Now, the more challenging part: we have to figure out how many arrangements there are involving C & E sitting together. This is a tricky problem to frame, so I’ll demonstrate the steps to follow. First, let’s look at the seats these two could be next to each other. There are four possible pairs of seats in which they could be next to each other
i. X X _ _ _
ii. _ X X _ _
iii. _ _ X X _
iv. _ _ _ X X
In each of those four cases, we could have either CE or EC, either order, so that’s 4 x 2 = 8 ways we could have just C & E sitting next to each other with the remaining three seats empty.
For the final step, we need to consider the other three children, A & B & D. In each of the eight cases, there are three blank seats waiting for those three, and those three could be put in any order in those blank seats. Three elements in any order—that’s 3! = 6. Thus, the total number of arrangements in which C & E would be next to each other would be 8 x 6 = 48. This is our numerator.
The probability would be this number, 48, over the total number of arrangements of the children, 120.
Most Upvoted Answer
Five children,Anaxagoras,Beatrice,Childeric,Desdemona, andEthelred, si...
Understanding the Problem
To find the probability that Childeric and Ethelred sit next to each other among five children, we can use combinatorial methods.
Total Arrangements
- There are 5 children, which can be arranged in 5! (factorial) ways.
- 5! = 120 total arrangements.
Grouping Childeric and Ethelred
- To simplify the problem, we can treat Childeric and Ethelred as a single unit or block.
- This block can be arranged in two ways: Childeric next to Ethelred or Ethelred next to Childeric.
Calculating the Block Arrangements
- By treating Childeric and Ethelred as one block, we effectively have 4 units to arrange: (CE), Anaxagoras, Beatrice, and Desdemona.
- The arrangements can be calculated as 4! = 24 ways.
Arranging the Block
- Since the block (CE) can be arranged in 2 ways (CE or EC), the total arrangements for this case are:
- Total = 4! * 2 = 24 * 2 = 48 arrangements.
Calculating the Probability
- The probability that Childeric and Ethelred sit next to each other is the number of favorable arrangements divided by the total arrangements.
- Probability = 48 (favorable) / 120 (total) = 48/120 = 2/5.
Final Result
- Therefore, the probability that Childeric and Ethelred sit next to each other is 2/5.
This aligns with option 'D'.
To find the probability that Childeric and Ethelred sit next to each other among five children, we can use combinatorial methods.
Total Arrangements
- There are 5 children, which can be arranged in 5! (factorial) ways.
- 5! = 120 total arrangements.
Grouping Childeric and Ethelred
- To simplify the problem, we can treat Childeric and Ethelred as a single unit or block.
- This block can be arranged in two ways: Childeric next to Ethelred or Ethelred next to Childeric.
Calculating the Block Arrangements
- By treating Childeric and Ethelred as one block, we effectively have 4 units to arrange: (CE), Anaxagoras, Beatrice, and Desdemona.
- The arrangements can be calculated as 4! = 24 ways.
Arranging the Block
- Since the block (CE) can be arranged in 2 ways (CE or EC), the total arrangements for this case are:
- Total = 4! * 2 = 24 * 2 = 48 arrangements.
Calculating the Probability
- The probability that Childeric and Ethelred sit next to each other is the number of favorable arrangements divided by the total arrangements.
- Probability = 48 (favorable) / 120 (total) = 48/120 = 2/5.
Final Result
- Therefore, the probability that Childeric and Ethelred sit next to each other is 2/5.
This aligns with option 'D'.
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Five children,Anaxagoras,Beatrice,Childeric,Desdemona, andEthelred, sit randomly in five chairs in a row. What is the probability that Childeric and Ethelred sit next to each other?a)1/30b)1/15c)1/5d)2/5e)7/20Correct answer is option 'D'. Can you explain this answer? for CLAT 2025 is part of CLAT preparation. The Question and answers have been prepared according to the CLAT exam syllabus. Information about Five children,Anaxagoras,Beatrice,Childeric,Desdemona, andEthelred, sit randomly in five chairs in a row. What is the probability that Childeric and Ethelred sit next to each other?a)1/30b)1/15c)1/5d)2/5e)7/20Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CLAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Five children,Anaxagoras,Beatrice,Childeric,Desdemona, andEthelred, sit randomly in five chairs in a row. What is the probability that Childeric and Ethelred sit next to each other?a)1/30b)1/15c)1/5d)2/5e)7/20Correct answer is option 'D'. Can you explain this answer?.
Five children,Anaxagoras,Beatrice,Childeric,Desdemona, andEthelred, sit randomly in five chairs in a row. What is the probability that Childeric and Ethelred sit next to each other?a)1/30b)1/15c)1/5d)2/5e)7/20Correct answer is option 'D'. Can you explain this answer? for CLAT 2025 is part of CLAT preparation. The Question and answers have been prepared according to the CLAT exam syllabus. Information about Five children,Anaxagoras,Beatrice,Childeric,Desdemona, andEthelred, sit randomly in five chairs in a row. What is the probability that Childeric and Ethelred sit next to each other?a)1/30b)1/15c)1/5d)2/5e)7/20Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CLAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Five children,Anaxagoras,Beatrice,Childeric,Desdemona, andEthelred, sit randomly in five chairs in a row. What is the probability that Childeric and Ethelred sit next to each other?a)1/30b)1/15c)1/5d)2/5e)7/20Correct answer is option 'D'. Can you explain this answer?.
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