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Question
The number of ways can 7 boys be seated at a round table so that 2 particular boys are next to each other is:-
The number of ways can 7 boys be seated at a round table so that 2 particular boys are next to each other is:-
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Solution
The correct option is C 5!2!
Step 1− seat one of the two particular boys at a seat, any seat. Since it is a circular table, there is only 1 way to do this (as all of the chairs are equivalent until someone is already sitting).Step 2− seat the second of the two particular boys. He must sit next to the first particular boy, so there are only two options available (the seat to the left, or the seat to the right of the first boy).Step 3− seat the remaining 5 boys in the remaining 5 chairs. There are 5! ways to do this.Combining all steps: 1×2!5!=5!2! total arrangements.
Step 1− seat one of the two particular boys at a seat, any seat. Since it is a circular table, there is only 1 way to do this (as all of the chairs are equivalent until someone is already sitting).
Step 2− seat the second of the two particular boys. He must sit next to the first particular boy, so there are only two options available (the seat to the left, or the seat to the right of the first boy).
Step 3− seat the remaining 5 boys in the remaining 5 chairs. There are 5! ways to do this.
Combining all steps: 1×2!5!=5!2! total arrangements.
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