In how many ways can 15 people be seated around two round tables with seating capacities of 7 and 8 people? Choose the correct option:
A) 15! /8!	B) 7! *8!	C) 15C7 *6! *7!	D) 2 * 15C7 *6! *7!	E) 15C8 *8!
Solution:   'n' objects can be arranged around a circle in (n−1)! ways.   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:   (7−1)! =6!   The remaining 8 people can be made to sit around the second circular table in: (8−1)! =7! Ways.   Hence, total number of ways: 15C7 *6! *7!.   Answer: Option 15C7 *6! *7!
<result>C</result>
In how many ways can 15 people be seated around two round tables with seating capacities of 7 and 8 people?