Ants problem involving combinatorics.

[shakgoku]

1. There are x distinguishable ants and there are x pots full of food. Due to the smell, the ants arrange themselves in a circle on the circular rim of each pot. In how many ways can they do this?

note:
Any number of pots can be free of ants. For example all the ants can be on the circular rim of a single pot. and ,

suppose, x = 3 and all the ants 1, 2 and 3 arrange themselves around a circle in clockwise as
123, 231, 312 are considered equivalent. and counted as 1configuration.

Homework Equations

3. suppose, all the ants on a single rim of the pot, the number of configurations is (x-1)! but, can't extend it to more general case, which is the problem

 

[LightHero]

here.Answer:The number of ways the ants can arrange themselves in a circle on the circular rim of each pot is (x-1)! x^(x-1).