To determine the total number of call letter arrangements possible under the given conditions, we must apply the fundamental counting principle step-by-step:
1. First Letter: The first letter must be either 'W' or 'K', so we have 2 choices.
2. Second Letter: For the second letter, we can choose any one of the remaining 25 letters (since the alphabet consists of 26 letters and we have already used one).
3. Third Letter: For the third letter, we can choose any one of the 24 letters left after selecting the first two.
4. Fourth Letter: For the fourth letter, we can choose any one of the 23 letters left after selecting the first three.
Thus, according to the fundamental counting principle, we multiply the number of choices for each letter together:
[tex]\[ 2 \cdot 25 \cdot 24 \cdot 23 \][/tex]
Carrying out this multiplication step-by-step, we have:
[tex]\[ 2 \cdot 25 = 50 \][/tex]
[tex]\[ 50 \cdot 24 = 1200 \][/tex]
[tex]\[ 1200 \cdot 23 = 27,600 \][/tex]
So, the total number of call letter arrangements possible is 27,600. Therefore, the correct equation that shows how the fundamental counting principle can be applied to determine the total number of call letter arrangements is:
[tex]\[ 2 \cdot 25 \cdot 24 \cdot 23 = 27,600 \][/tex]
Thus, the correct answer to the question is:
[tex]\[ 2 \cdot 25 \cdot 24 \cdot 23=27,600 \][/tex]
