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Radio station call letters must begin from either K or W and have two or three additional letters.

Thecounting rule involving the multiplication of cases at each step is useful in computingthe total number of possibilities/outcomes of an event.

For the first letter, only K or W are the possibilities.

Thus, the total number of possibilities is two.

Case 1: There are two additional letters.

The number of possibilities for each of the two additional letters is 26.

The total number of possibilities for all three letters is

$2脳26脳26=1352$

Case 2: There are three additional letters.

The number of possibilities for each of the three additional letters is 26.

The total number of possibilities for all four letters is

$2脳26脳26脳26=35152$

The total number of possibilities for the letters is the sum of the possibilities of cases 1 and 2.

$$\begin{gathered} \text{Total}\text{possibilities}=\text{1352}+\text{35152} \\ =\text{36504} \end{gathered}$$

Therefore, the total number of different possibilities when the call letter begins with either K or W and contains two or three more additional letters is equal to 36504.