The population of Carlisle, Pennsylvania, is about 20,000. If each resident has three initials, is it true that there must be at least two residents with the same initials? Give a justification of your answer.

TRUE. There are 20,000 inhabitants and by the product rule (in literature also known as the multiplication principle and shortened to MP) there are \(26^3 = 17576\) possibilities for 3 initials which is less than the number of inhabitants so some of the inhabitants must share the inititals.