No of circular arrangement(permutations) of n different things = (n-1)!
Question: In how many ways can 6 people be seated around a circular table for dinner?
Solution:
Step 1:
Since the people are seated around the circular table we take,
(n-1)!
Here, n = 6
Step 2:
(6 – 1)! = 5! = 120
Therefore, 6 people can sit in 120 ways around a circular table.
Number of circular arrangement of n different things when a clockwise and a anticlockwise arrangements are not different that is when observation can be made from both sides
\[\frac{(n-1)!}{2}\]
The garland can be made in anti-clockwise and clockwise direction. As clockwise and anti-clockwise direction is considered to be the same, we take,
½ (n -1)!
Here n = 12
Step 2:
½ (12 – 1)! =
11!/ 2
Therefore, In 11!/ 2 ways can be found to make garlands from 12 different coloured flowers.
