After the heavenly race, each sign went back to a month of the year, but without caring whether it was "its" month, or if there already were other signs in that month.

In how many ways can the signs be assigned to months in this way? Isn't this the same answer as in that problem? Why/why not?

There are 12^12 ways of assigning signs of the zodiac to months with repitition allowed with the simple logic that each sign can be assigned one of twelve months.

This is not analagous to the heavenly race case where assignment had to do with order. An example of a difference would be in the race all participants might tie which would represent one outcome whereas in this month assignment case all signs might be assigned to the same month which can happen in twelve ways. 

Posted by Eric on 2006-12-05 14:18:44