4. The Generalized Pigeonhole Principle states that for any function f from a finite set X to a finite set Y and for any positive integer k, if n(X) > k · n(Y), then there is some y in Y such that y is the image of at least k + 1 distinct elements of X.
Here let X be the set of people and Y be the set of astrological star signs. What is the size of the set Y? How large can the integer k be in order to apply the generalized pigeonhole principle?