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Sagot :
Answer:
Step-by-step explanation:
To determine the number of possible four-letter sets for television and radio stations, let's break down the problem.
1. **First Letter:**
- The first letter must be either \( W \) or \( K \).
- This gives us 2 choices for the first letter.
2. **Second, Third, and Fourth Letters:**
- These letters must be from \( L \) to \( Z \), inclusive.
- The number of letters from \( L \) to \( Z \) is \( 26 - 11 = 15 \) (since \( L \) is the 12th letter and \( Z \) is the 26th letter, the range from \( L \) to \( Z \) includes 15 letters).
3. **No Repetitions:**
- Since there are no repetitions allowed in the second to fourth letters, we need to count the permutations of 3 letters out of these 15.
The number of ways to choose and arrange 3 letters out of 15 (permutations) is given by \( P(15, 3) \), which can be calculated as:
\[
P(15, 3) = 15 \times 14 \times 13
\]
Now, multiply this by the 2 choices for the first letter:
\[
2 \times (15 \times 14 \times 13)
\]
Let's calculate this step by step:
1. Calculate the number of permutations for the second to fourth letters:
\[
15 \times 14 = 210
\]
\[
210 \times 13 = 2730
\]
2. Multiply by the 2 choices for the first letter:
\[
2 \times 2730 = 5460
\]
Thus, the number of possible four-letter sets is \( 5460 \).
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