Question

18 guests have to be seated , half on each side of a long table.4 particular guests desire to sit on 1 particular side and 3 others on the other side .Deter Dete the number of ways in which the sitting arrangement can be done.

Answer 1

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.