Question

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 repetition are allowed?

Answer 1

\[2\times 25\times 24\times 23\] for the first one

Answer 2

second one is
\[2\times 26\times 26\times 26\]

Answer 3

thanks but how did u get that?

Answer 4

Consider the first letter, it is a W or a K. So far, you have two options.
Then, consider the second, if you are not allowed repetition, then you will have 25 letters left (since you already used W or K). So we have 2*25 options so far, since for whatever first letter we choose, we still have 25 choices for second letter.
The same reasoning allows us to conclude that for the third letter, there will be 24 choices, giving 2*25*24 option, and 2*25*24*23 choices for four letters.
If we allow repetitions, we do the same thing, but don't rule out used letter as we go along.

Answer 5

ohhh ok thanks