Three boys and three girls are to be seated around a table

Question

Three boys and three girls are to be seated around a table in a circle. Among boys, X does not want any girl neighbor and among girls Y does not want any boy neighbor. How many such arrangements are possible?

A) 6
B) 4
C) 8
D) 2
E) 9

A) 6
B) 4
C) 8
D) 2
E) 9

chetan2u · Answer

Hi..
 This basically means all three boys have to be together with X in center and three girls together with Y in center. 
X and Y have there seats fixed. The remaining boys can be seated in 2! Ways and similarly girls in 2! Ways..
Total 2*2=4
B

arvind910619 · Answer

Hi why it can not be 8 as the we can divide 6 seats in 2 different ways.
please explain fault in my reasoning?

ganand · Answer

Hi  arvind910619 ,

It can't be 8 because the question is about the circular arrangement. In the case of a linear arrangement, it would be 8.

Please refer the attached diagram. Both arrangments are essentially same. If you rotate the first diagram you will get the second diagram.

Hope it helps.
Thanks.

ScottTargetTestPrep · Answer

Since none of the given answer choices is more than 10, we can list all the arrangements. We can let A and B be the remaining two boys and C and D be the remaining two girls.

Since X doesn’t want to sit next to a girl, he must sit between A and B. Since Y doesn’t want to sit next to a boy, she must sit between C and D. Therefore, we can have the following arrangements:

A-X-B-C-Y-D
B-X-A-C-Y-D
A-X-B-D-Y-C
B-X-A-D-Y-C

We see that there are 4 seating arrangements.

Answer: B

Three boys and three girls are to be seated around a table

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