EXAMPLE 34 Counting with repetition: Famous initials

Some Americans in history are uniquely identified by their initials. For example, “JFK” stands for John Fitzgerald Kennedy, and “FDR” stands for Franklin Delano Roosevelt. How many different possible sets of initials are there for people with a first, middle, and last name?

Solution

Let us consider the three initials as an activity consisting of three events. Note that a particular letter may be repeated, as in “AAM” for A. A. Milne, author of Winnie the Pooh. Then there are ways to choose the first initial, ways to choose the second initial, and ways to choose the third initial. Thus, by the Multiplication Rule for Counting, the total number of different sets of initials is