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?

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