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 on the list and Y be the set of combinations of first and last initials. There are 26 letters in the alphabet, so there are 26×26 = 676 combinations of initials (so n(Y) = 676). We have 680 people (so n(X) = 680) on the list, so by the pigeonhole principle there must be at least two people who have the same first and last initials.