1.  In how many ways can 15 people be seated around two round tables with seating capacities of 7 and 8 people?
A. 15!/(8!)
B. 7!*8!
C. 15C8 x 6! x 7!
D. 2*(15C7)*6!*7!

Answer: Option C

Explanation:

Circular Permutation

'n' objects can be arranged around a circle in (n1)!

If arranging these 'n' objects clockwise or counter clockwise means one and the same, then the number arrangements will be half that number.

i.e., number of arrangements =  (n - 1)!
2

You can choose the 7 people to sit in the first table in 15C7 ways.

After selecting 7 people for the table that can seat 7 people, they can be seated in: (71)! = 6!

The remaining 8 people can be made to sit around the second circular table in: (81)! =7! Ways.

Hence, total number of ways: 15C8 × 6! × 7!