in a group of 700 people, must there be 2 who have matching first and last initials? why? (assume each person has a first and last name, and the initials are from the 26 letters of the roman alphabet.) to answer this question, let a be the set of the 700 distinct people and let b be the set consisting of all possible combinations of first and last initials. then b has elements. so, if a function is constructed from a to b that relates each of the 700 people to their initials, then by the pigeonhole principle, the function is onto . therefore, in a group of 700 people, it is ---select--- that no two people have matching first and last initials. so the answer to the question is ---select--- .