﻿ There are 20 persons among whom are two brothers. Find the number of ways in which we can arrange them around a circle so that there is exactly one person between the two brothers. : Kaysons Education

# There Are 20 Persons Among Whom Are Two Brothers. Find The Number Of Ways In Which We Can Arrange Them Around A Circle So That There Is Exactly One Person Between The Two Brothers.

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## Question

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Correct option is

× 18!.

Let B1 and B2 be two brothers among 20 persons and let M be a person that will sit between B1 and B2. The person can be chosen from 18 persons (excluding B1 and B2) in 18 ways. Considering the two brothersB1 and B2 and person M as one person, we have 18 persons in all. These 18 persons can be arranged around a circle in (18 – 1)! = 17! Ways.

But B1 and B2 can be arranged among themselves in 2! = ways

Hence the total number of ways = 18 × 17! × 2!. = 2 × 18!.

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