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10 persons are seated around a round table. What is the probability that 4 particular persons are always seated together?
- a)1/21
- b)4/21
- c)8/21
- d)11/21
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
10 persons are seated around a round table. What is the probability th...
Total outcomes = (10 -1)! = 9!
Favourable outcomes = 6!*4! (4 person seated together and 6 other persons seated randomly, so they will sit in (7-1)! Ways and those 4 persons can be arranged in 4! ways)
So probability = 1/21
Favourable outcomes = 6!*4! (4 person seated together and 6 other persons seated randomly, so they will sit in (7-1)! Ways and those 4 persons can be arranged in 4! ways)
So probability = 1/21
Most Upvoted Answer
10 persons are seated around a round table. What is the probability th...
To find the probability that 4 particular persons are always seated together, we can consider them as a single entity and calculate the total number of ways the remaining 6 persons can be seated around the table.
Total number of ways to seat 10 persons around a round table = (10-1)! = 9!
Now, let's consider the 4 particular persons as a single entity. So, we have 7 entities to be seated around the table.
Total number of ways to seat 7 entities around a round table = (7-1)! = 6!
Within this arrangement, the 4 particular persons can be seated among themselves in 4! ways.
Therefore, the total number of ways the 4 particular persons are always seated together = 6! * 4!
Now, let's calculate the probability:
Probability = (Total number of ways the 4 particular persons are always seated together) / (Total number of ways to seat 10 persons around the table)
Probability = (6! * 4!) / 9!
Simplifying the expression:
Probability = (6 * 5 * 4 * 3 * 2 * 4 * 3 * 2) / (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)
Canceling out common terms:
Probability = (4 * 3 * 2) / (9 * 8 * 7)
Probability = 24 / 504
Reducing the fraction:
Probability = 1 / 21
Therefore, the correct answer is option A) 1/21.
Total number of ways to seat 10 persons around a round table = (10-1)! = 9!
Now, let's consider the 4 particular persons as a single entity. So, we have 7 entities to be seated around the table.
Total number of ways to seat 7 entities around a round table = (7-1)! = 6!
Within this arrangement, the 4 particular persons can be seated among themselves in 4! ways.
Therefore, the total number of ways the 4 particular persons are always seated together = 6! * 4!
Now, let's calculate the probability:
Probability = (Total number of ways the 4 particular persons are always seated together) / (Total number of ways to seat 10 persons around the table)
Probability = (6! * 4!) / 9!
Simplifying the expression:
Probability = (6 * 5 * 4 * 3 * 2 * 4 * 3 * 2) / (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)
Canceling out common terms:
Probability = (4 * 3 * 2) / (9 * 8 * 7)
Probability = 24 / 504
Reducing the fraction:
Probability = 1 / 21
Therefore, the correct answer is option A) 1/21.
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10 persons are seated around a round table. What is the probability th...
Correct answer is option 'A'
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