If radio station call letters must begin with either K or W and must include either two or three additional letters, how many different possibilities are there?

36,504

2(26^2 + 26^3) = ?

To determine the number of different possibilities, you need to consider the number of options for the first letter (K or W) and the number of options for the remaining two or three letters.

For the first letter, there are 2 possibilities (K or W).

For the remaining two or three letters, we have 26 options for each letter because there are 26 letters in the English alphabet (excluding K and W in this case).

If we assume the call letters include two additional letters:
- The first additional letter has 26 options.
- The second additional letter also has 26 options.

So, for two additional letters, there are 26 * 26 = 676 possibilities.

If we assume the call letters include three additional letters:
- The first additional letter has 26 options.
- The second additional letter has 26 options.
- The third additional letter also has 26 options.

So, for three additional letters, there are 26 * 26 * 26 = 17,576 possibilities.

Now, we can calculate the total number of different possibilities by summing up the possibilities for two and three additional letters:
2 (choices for the first letter) * [26 (choices for two additional letters) + 26 * 26 (choices for three additional letters)]
= 2 * [26 + 26 * 26] = 2 * 702 = 1,404

Therefore, there are 1,404 different possibilities for radio station call letters that begin with either K or W and include either two or three additional letters.