wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If 8 persons A,B,C,D,E,F,G,H are to be seated around a circular table, then the number of possible arrangements

A
without any restriction is 7!
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
when A and B should be seated together is 6!
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
when A and B should be seated opposite to each other is 6!
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
when there should be exactly two persons between A and B is 720
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C when A and B should be seated opposite to each other is 6!
Number of ways to arrange n persons in circular table is (n1)! ways
Total ways without any restriction is (81)!=7!

When A and B should be seated together
Consider A and B as one unit.
when A and B should be seated together is 6!×2!
(A and B can interchange among themselves)

When A and B should be seated opposite to each other.
Let A select the seat, it can be done in 1 way (because it is circular table)
B can select the seat in 1 way opposite to A.
Now the remaining persons can be arranged in 6! ways.
Total ways are 1×1×6!

When there should be exactly two persons between A and B
Let the two persons be arranged in between A and B in 6C2×2! ways.
The remaining 4 places can be occupied in 4! ways.
Also, since A and B can also interchange among themselves.
Total ways
= 6C2×2!×2!×4!=1440

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon