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5 persons are sitting in a round table in such way that Tallest Person is always on the right– side of the shortest person; the number of such arrangements is
- a)6
- b)8
- c)24
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
5 persons are sitting in a round table in such way that Tallest Person...
There are 5 persons,so total arrangements in case of circular permutation is (n-1)!,
Here according to the condition tallest person is always right of shortest person(note: there is only one tallest and shortest person).
Therefor take both tallest and shortest person as one person so we have 4 persons.
Total arrangements of 4 person is
(4-1)! . That is 3!
Answer is 6
Most Upvoted Answer
5 persons are sitting in a round table in such way that Tallest Person...
Solution:
Given, there are 5 persons sitting in a round table in such a way that the tallest person is always on the right side of the shortest person.
Let us assume the shortest person to be seated at the top of the table. Then, the tallest person can be seated only to his right side.
Now, the remaining 3 persons can be seated in any way around the table.
Therefore, the number of such arrangements = 3! = 6
Hence, the correct answer is option A) 6.
Given, there are 5 persons sitting in a round table in such a way that the tallest person is always on the right side of the shortest person.
Let us assume the shortest person to be seated at the top of the table. Then, the tallest person can be seated only to his right side.
Now, the remaining 3 persons can be seated in any way around the table.
Therefore, the number of such arrangements = 3! = 6
Hence, the correct answer is option A) 6.
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Community Answer
5 persons are sitting in a round table in such way that Tallest Person...
We are asked to find the number of ways in which 5 persons can sit at a round table such that the tallest person is always to the right of the shortest person.
Step 1: Total Number of Arrangements without Any Restrictions
In a round table arrangement, the number of ways to arrange n persons is given by (n - 1)! because the arrangement is circular (rotations of the same arrangement are considered identical).
In a round table arrangement, the number of ways to arrange n persons is given by (n - 1)! because the arrangement is circular (rotations of the same arrangement are considered identical).
For 5 persons, the total number of ways to arrange them without any restriction is:
(5 - 1)! = 4! = 4 × 3 × 2 × 1 = 24
Step 2: Fixing the Positions of the Tallest and Shortest Persons
Since the tallest person must always be on the right side of the shortest person, we need to ensure that this condition is satisfied.
In a circular arrangement, if we fix the position of the shortest person (since the table is round, we can consider one position as fixed), there is only one specific seat to the right of the shortest person where the tallest person can sit. So, the tallest person's seat is fixed once we fix the shortest person's position.
(5 - 1)! = 4! = 4 × 3 × 2 × 1 = 24
Step 2: Fixing the Positions of the Tallest and Shortest Persons
Since the tallest person must always be on the right side of the shortest person, we need to ensure that this condition is satisfied.
In a circular arrangement, if we fix the position of the shortest person (since the table is round, we can consider one position as fixed), there is only one specific seat to the right of the shortest person where the tallest person can sit. So, the tallest person's seat is fixed once we fix the shortest person's position.
Step 3: Arranging the Remaining 3 Persons
Once the shortest and tallest persons are seated, the remaining 3 persons can be arranged in the remaining 3 positions. The number of ways to arrange these 3 persons is:
3! = 3 × 2 × 1 = 6
Once the shortest and tallest persons are seated, the remaining 3 persons can be arranged in the remaining 3 positions. The number of ways to arrange these 3 persons is:
3! = 3 × 2 × 1 = 6
Step 4: Final Calculation
Since we have fixed the positions of the shortest and tallest persons and can arrange the other 3 persons in 6 ways, the total number of valid arrangements is: 6
Final Answer:
The number of ways to arrange 5 persons at a round table such that the tallest person is always on the right side of the shortest person is 6.
Since we have fixed the positions of the shortest and tallest persons and can arrange the other 3 persons in 6 ways, the total number of valid arrangements is: 6
Final Answer:
The number of ways to arrange 5 persons at a round table such that the tallest person is always on the right side of the shortest person is 6.
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5 persons are sitting in a round table in such way that Tallest Person is always on the right– side of the shortest person; the number of such arrangements isa)6b)8c)24d)none of theseCorrect answer is option 'A'. Can you explain this answer?
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