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A round table conference is to be held between 20 delegates. How many seating arrangements are possible if two particular delegates are always separated by exactly one person.Please help me with this question.

A round table conference is to be held between 20 delegates. How many seating arrangements are possible if two particular delegates are always separated by exactly one person.Please help me with this question.

Grade:11

1 Answers

RAKSHA A
33 Points
5 years ago
First, let us think abt the 3 delegates who have to arranged in a such a way that two of them are seperated by one particular delegate. So among the 3 of them, the delegate ( let it be C) who seperates the other 2 has a fixed position, i.e. between the other 2. Let the other two be A and B. there r 2 options to arrange them. A is to the right of C and B to the left of C and vise versa. So for A,B,C the no of possible arrangements is 2! ways. Now the remaining 17 delegates can be arranged in 16! ways by taking position of ABC as reference point. So totally, the arrangement is 16! * 2!. Hope you have understood.
 

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