5 persons are sitting in a round table in such way that Tallest Person...
I guess answer is c
tallest and shortest are fixed so considering them as 1 unit
remaining 3 can be seated in 3! ways
so 3+1=4!
4!=24
5 persons are sitting in a round table in such way that Tallest Person...
The given problem involves arranging 5 persons in a round table in a specific way, where the tallest person is always on the right side of the shortest person. We need to find the number of such arrangements.
Understanding the Problem:
We have 5 persons, and they need to be arranged in a round table. The tallest person should always be on the right side of the shortest person. This means that the shortest person will occupy the first position in the arrangement, and the tallest person will occupy the fifth position.
Approach:
To solve this problem, we can fix the position of the shortest person and then arrange the remaining 4 persons around the table. Let's consider the shortest person as Person A and the tallest person as Person E.
Step 1: Fix the position of Person A
Since Person A needs to be in the first position, we fix his position.
Step 2: Arrange the remaining 4 persons
Now, we have 4 persons remaining (B, C, D, and E) to be arranged around the table. However, we need to ensure that Person E (the tallest person) is always on the right side of Person A (the shortest person).
Case 1: Person E is to the immediate right of Person A
In this case, Person B, Person C, and Person D can be arranged in any order to the left of Person A. The arrangement for this case is as follows:
A -> E -> B -> C -> D
Case 2: Person E is not to the immediate right of Person A
In this case, Person B, Person C, Person D, and Person E can be arranged in any order to the left of Person A. The arrangement for this case is as follows:
A -> B -> E -> C -> D
Calculating the number of arrangements:
In Case 1, we have 3 persons (B, C, D) to be arranged, which can be done in 3! = 6 ways.
In Case 2, we have 4 persons (B, C, D, E) to be arranged, which can be done in 4! = 24 ways.
Since both cases are valid arrangements, we need to consider the total number of arrangements as the sum of the arrangements in both cases.
Total number of arrangements = Number of arrangements in Case 1 + Number of arrangements in Case 2
= 6 + 24
= 30
Therefore, the number of arrangements satisfying the given conditions is 30.
Answer:
(d) none of these
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