Television and radio stations use four call letters starting with W or K, such as WXYZ or KRLD. Assuming no repetitions in the second to forth letters, how many four-letter sets are possible issuing either W or K and only the letter L to Z



Answer :

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 \( 5460 \).