9010
chetan2u
Bunuel
Eighteen guests have to be seated, half on each side a long table. Four particular guest desires to sit on one particular side and three others on the other side. The number of ways in which the seating arrangement can be made, is
(A) \(9! *9!\)
(B) \(11C5 * 9! * 9!\)
(C) \((\frac{11!}{5!}) * 9! * 9!\)
(D) \(11C5\)
(E) \(11C5 * 9!\)
Are You Up For the Challenge: 700 Level QuestionsLet the two sides of table be A, where 4 are to seated, and B, where 3 are to be seated.
A: 4 are already seated
The remaining 5 can be chosen from 11 in 11C5.
B: 3 are already seated
The remaining 6 are already segregated above in 11C5.
Finally, 9 on each side can be arranged in 9! ways.
Total = 11C5*9!*9!
B
chetan2u Bunuel KarishmaBThere were two 11C5 (one for each side), then why you have taken only 1?? Experts Any alternative solution please.
When you take 11C5, it gives you two groups one of 5 and other of 6.
So if we calculate 11C5 for A and 11C6 for B, you are taking each combination twice.
Say the numbers are 1 to 11 and 1,2,3,4,5 are placed on table 1. The remaining six, 6,7,8,9,10,11 automatically move to table B.