please explain with theory/concept
a) In how many ways can 5 persons be seated around a circular table?
b) In how many ways can 5 people from a group of 6 people be seated around a circular table?
a) As it is round table, 5! cannot be the answer, because some arrangements will be the same
For example abcde = bcdea = cdeab = deabc = eabcd
There are 5 versions of each arrangement, so if we only wish to count for 1 version of this
\frac{5!}{5} = 4! = 24
b) There can be \frac{6!}{5! * 1!} combinations of people ie 6
All these 6 combinations can be arranged in \frac{5!}{5} ways ie 24
So, answer is 6 * 24 = 144