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. 15C7 × 6! × 7!
D. 2 × 15C7 × 6! × 7!
E. 15C8 × 8!
Answer: Option C
Solution(By Examveda Team)
'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 = $$\frac{{\left( {n - 1} \right)!}}{2}$$ 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!Join The Discussion
Comments ( 1 )
Related Questions on Permutation and Combination
A. 3! 4! 8! 4!
B. 3! 8!
C. 4! 4!
D. 8! 4! 4!
A. 7560,60,1680
B. 7890,120,650
C. 7650,200,4444
D. None of these
A. 8 × 9!
B. 8 × 8!
C. 7 × 9!
D. 9 × 8!
Why is (7-1)! Ways? Why the -1?