A radio station is identified by four call letters (e.g., KAGU). The first letter must be a K or W. How many different stations can be made if repeated letters are NOT allowed? There is a total of 26 letters in the English alphabet.
To calculate the number of different radio stations that can be made with four call letters, without allowing repeated letters, we can break it down into steps:
Step 1: Choose the first letter: The first letter must be either K or W, so there are 2 choices.
Step 2: Choose the second letter: After choosing the first letter, there are 25 remaining letters in the English alphabet (since we cannot repeat letters). Therefore, there are 25 choices for the second letter.
Step 3: Choose the third letter: After choosing the first and second letters, there are now 24 remaining letters (because we cannot repeat letters). So, there are 24 choices for the third letter.
Step 4: Choose the fourth letter: After choosing the first, second, and third letters, there are 23 remaining letters. Hence, there are 23 choices for the fourth letter.
To find the total number of different radio stations, we multiply the number of choices at each step:
Total number of radio stations = (Number of choices for the first letter) * (Number of choices for the second letter) * (Number of choices for the third letter) * (Number of choices for the fourth letter)
Total number of radio stations = 2 * 25 * 24 * 23
Calculating the above expression, we find that there are 2,760 different radio stations that can be made without repeating letters.