Question

Fifteen persons sit around a table. Find the number of arrangements that have two specified persons not sitting side by side.

Answer 1

Since 2 particular persons can’t be sitting side by side.
The other 13 persons can be arranged around the table in (13 − 1)! = 12!
13 people around a table create 13 gaps in which 2 person are to be seated
Number of arrangements of 2 person = ¹³P₂
∴ Total number of arrangements in which two specified persons not sitting side by side
= 12! × ¹³P₂
= 12 × 13 × 12
= 13 × 12! × 12
= 12 × 13!