Using the letters $A$ and $B$, the following two-letter code words can be formed: $AA$, $AB$, $BB$, $BA$. Using the letters $A$, $B$, and $C$, how many different three-letter code words can be formed?
To form a three-letter code word, I need to choose one letter for each of the three positions: first, second, and third. For each position, I have three possible choices: $A$, $B$, or $C$. So, the total number of code words is the product of the choices for each position: $3 \times 3 \times 3 = 27$. 