2. The pigeonhole principle states that given a function, f, from the set X to the set Y, where n(X) > n(Y), there must be at least two elements in the domain that have the same image in the co-domain.
Here let X be the set of people and Y be the set of combinations of first and last initials. What is the size of the set Y? Is the set X large enough to apply the pigeonhole principle?