Answered

The call letters 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?

Answer :

Answer: The answer is 27600 and 35152.

Step-by-step explanation:  Given that the call letters of a radio station must have 4 letters and the first letter is one of K or W. We are to calculate the number of call letters that can be made if repetition is allowed and not allowed.

If repetition is not allowed, then we can choose the first letter in 2 ways, second letter in 25 ways, third letter in 24 ways and fourth letter in 23 ways. So, the total number of call letters will be

[tex]N_{rna}=2\times 25\times 24\times 23=27600.[/tex]

If repetition is allowed, then we can choose the first letter in 2 ways, second letter in 26 ways, third letter in 26 ways and fourth letter in 26 ways. So, the total number of call letters will be

[tex]N_{ra}=2\times 26^3=35152.[/tex]

Thus, the required answer is 27600 and 35152.

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