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Eighteen guests have to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on the other side. Determine the number of ways in which the sitting arrangements can be made.

Eighteen guests have to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on the other side. Determine the number of ways in which the sitting arrangements can be made.

Grade:upto college level

2 Answers

Navjyot Kalra
askIITians Faculty 654 Points
6 years ago
Hello Student,
Please find the answer to your question
Out of guests half i.e. to be seated on side A and rest 9 on side B. Now out of 18 guests, 4 particular guests desire to sit – on one particular side say side A and other 3 on other side B. Out of rest 18 – 4 – 3 = 11 guests we can select 5 more for side A and rest 6 can be seated on side B. Selection of 5 out of 11 can be done in 11 C5 ways and 9 guests on each sides of table can be seated in 9! x 9! Ways. Thus there are total 11 C5 x 9! x 9! Arrangements.

Thanks
navjot kalra
askIITians Faculty
jainish savalia
11 Points
3 years ago
8 on side A and side B. In side A 4 particular are to be seated therefore its arrangement out of 8 is = 4!*5! (4! is
 internal arrangement).
 
In the same way on side B 3 particular are to be seated therefore its arrangement out of 8 is = 3!*6!
 
remaining 4 seats in A and 5 seats in B its arrangement out of 9 places is 9!
also, this arrangement can be placed in two ways A placed before B and B placed before A.
 
hence total arrangements are =2*4!*5!*3!*6!*9!

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