The call letter of a radio station must have 4 letters.The first letter must be a K or a W. How many different station call letters can be made if repetitions are not allowed? *(If repetitions are allowed?)*
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To calculate the number of different station call letters that can be made, we can use the concept of permutations.
If repetitions are not allowed, we can consider the following cases:
Case 1: The first letter is 'K'
In this case, we have one option for the first letter ('K') and 25 options for each of the remaining three letters. So, the total number of call letters is 1 * 25 * 24 * 23 = 13,800.
Case 2: The first letter is 'W'
Similarly, in this case, we have one option for the first letter ('W') and 25 options for each of the remaining three letters. So, the total number of call letters is also 1 * 25 * 24 * 23 = 13,800.
Therefore, when repetitions are not allowed, the total number of different station call letters that can be made is 13,800 + 13,800 = 27,600.
If repetitions are allowed, we need to consider all combinations for each position:
For each position (except the first one), we have 26 options (26 letters of the alphabet). However, since we have already used 'K' or 'W' for the first letter, we have only 25 options for the first position. So, the total number of call letters when repetitions are allowed is 2 * 25 * 26 * 26 = 33,800.
In summary:
- When repetitions are not allowed, there are 27,600 different station call letters.
- When repetitions are allowed, there are 33,800 different station call letters.