Radio stations in the United States have call letters that begin with either K or W.

Question

Radio stations in the United States have call letters that begin with either K or W. Some have three letters; others have four letters. How many three-letter call letters are possible? How many four-letter call letters are possible?

Answer 1

Hello!

To solve this we simply look at the number of possibilities for each letter and multiply them together.

To find the number of three call letters we have to consider three letters:

The first letter can only be K or W, so it has 2 options.

The second and third letters can be any letter in the alphabet so they EACH have 26 options.

To find the total number of options we multiply the number of options for each letter:

2 * 26 * 26 = 1352

Adding a fourth letter means another letter with 26 options. We can take our previous value and simply multiply by 26.

1352 * 26 = 35152