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A and B are two persons sitting in a circular arrangement with 8 other persons. Find the probability that both A and B sit together.
- a)1/9
- b)2/7
- c)2/9
- d)2/5
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A and B are two persons sitting in a circular arrangement with 8 other...
Method to Solve :
As this is a case of circular permutations, ten people randomly be arranged around a circular table in (n-1)! = (10–1)! = 9! ways.
Since 2 particular people are always together consider them as one person say P. Now, P with other 8, so 9 can be arranged around the table in 8! ways. The two between themselves can arranged in 2! ways.
Hence the required probability is 8! 2!/9! = 2/9
Since 2 particular people are always together consider them as one person say P. Now, P with other 8, so 9 can be arranged around the table in 8! ways. The two between themselves can arranged in 2! ways.
Hence the required probability is 8! 2!/9! = 2/9
Most Upvoted Answer
A and B are two persons sitting in a circular arrangement with 8 other...
To find the probability that both A and B sit together in a circular arrangement, we need to consider them as a single entity. Let's call this entity AB.
Total number of ways to arrange 10 people in a circle = (10-1)! = 9!
Now, when A and B sit together, we can consider them as a single entity AB. So, we have 9 entities to arrange in a circle.
Number of ways to arrange 9 entities in a circle = (9-1)! = 8!
Within the entity AB, A and B can be arranged in 2 ways (AB or BA).
Therefore, the total number of ways A and B can sit together in a circle = 8! * 2
Probability = Number of favorable outcomes / Total number of outcomes
Probability = (8! * 2) / 9!
Simplifying,
Probability = 2/9
Hence, the correct answer is option C, 2/9.
Total number of ways to arrange 10 people in a circle = (10-1)! = 9!
Now, when A and B sit together, we can consider them as a single entity AB. So, we have 9 entities to arrange in a circle.
Number of ways to arrange 9 entities in a circle = (9-1)! = 8!
Within the entity AB, A and B can be arranged in 2 ways (AB or BA).
Therefore, the total number of ways A and B can sit together in a circle = 8! * 2
Probability = Number of favorable outcomes / Total number of outcomes
Probability = (8! * 2) / 9!
Simplifying,
Probability = 2/9
Hence, the correct answer is option C, 2/9.
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