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The total number of sitting arrangements of 7 persons in a row if 3 persons sit together in a particular order is _________.
- a)5!
- b)6!
- c)2! X 5!
- d)None
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The total number of sitting arrangements of 7 persons in a row if 3 pe...
Given: 7 persons, 3 persons sit together in a particular order
To find: Total number of sitting arrangements
Solution:
Let the 3 persons sitting together be treated as a single entity.
Then, we have 5 entities to be arranged in a row.
The number of ways of arranging n entities in a row is n!.
Therefore, the number of ways of arranging 5 entities in a row is 5!.
But the 3 persons sitting together can also be arranged among themselves in 3! ways.
Therefore, the total number of sitting arrangements is 5! × 3! = 720.
Hence, the correct option is (a) 5!.
To find: Total number of sitting arrangements
Solution:
Let the 3 persons sitting together be treated as a single entity.
Then, we have 5 entities to be arranged in a row.
The number of ways of arranging n entities in a row is n!.
Therefore, the number of ways of arranging 5 entities in a row is 5!.
But the 3 persons sitting together can also be arranged among themselves in 3! ways.
Therefore, the total number of sitting arrangements is 5! × 3! = 720.
Hence, the correct option is (a) 5!.
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Community Answer
The total number of sitting arrangements of 7 persons in a row if 3 pe...
Heyya!
In the question it is asked particular order Total 7 persons are seated in such a way that 3persons sit together.
So, Firstly name the 7 persons as A, B, C, D, E, F and G
Let's say EFG have to sit together.
So the Arrangement will be:
_ 1 _ 2 _ 3 _ 4_ ( E F G) {EFG have to sit together so, these will be marked as 1person.
So, now there will be 5 arrangements (5persons) {EFG regarded as 1 person}
So, the number if ways these can be arranged are 5!
Hence, 5! is the answer.
Hope you got it!
All the best!
>Gk
In the question it is asked particular order Total 7 persons are seated in such a way that 3persons sit together.
So, Firstly name the 7 persons as A, B, C, D, E, F and G
Let's say EFG have to sit together.
So the Arrangement will be:
_ 1 _ 2 _ 3 _ 4_ ( E F G) {EFG have to sit together so, these will be marked as 1person.
So, now there will be 5 arrangements (5persons) {EFG regarded as 1 person}
So, the number if ways these can be arranged are 5!
Hence, 5! is the answer.
Hope you got it!
All the best!
>Gk
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