1. Tardigrade
  2. Question
  3. Mathematics
  4. Six persons A, B, C, D, E and F are to be seated at a circular table. The number of ways, this can be done if A must have either B or C on his right and B must have either C or D on his right is

Q. Six persons A, B, C, D, E and F are to be seated at a circular table. The number of ways, this can be done if A must have either B or C on his right and B must have either C or D on his right is

 3051  233 Permutations and Combinations Report Error

Solution:

When A has B or C to his right we have the order : AB or AC ...(1)
When B has C or D to his right, we have the order : BC or BD ...(2)
Taking these two possibilities together, we must have ABC or ABD or AC and BD.
For ABC, D, E, F to arrange along a circle, number of way = 3 ! = 6, where three persons A,B,C together are treated as single.
For ABD, C, E, F, the number of ways = 6. For AC, BD, E,F the number of ways = 6.
Hence, total number of ways = 18.