Question

how many different arrangements of 3 letters can be formed if the first letter must be w or k (repeats of letters are allowed)?
there are \\(\square\\) different 3-letter combinations that can be formed.
(simplify your answer.)

Explanation:

Step1: Determine the number of choices for the first letter

The first letter must be \(W\) or \(K\), so there are \(2\) choices for the first letter.

Step2: Determine the number of choices for the second and third letters

Since repeats are allowed and there are \(26\) letters in the alphabet, there are \(26\) choices for the second letter and \(26\) choices for the third letter.

Step3: Use the multiplication principle

The multiplication principle states that if there are \(m\) ways to do one thing, \(n\) ways to do a second thing, and \(p\) ways to do a third thing, then there are \(m\times n\times p\) ways to do all three things.
Here, \(m = 2\) (choices for the first letter), \(n=26\) (choices for the second letter), \(p = 26\) (choices for the third letter).
The total number of arrangements is \(2\times26\times26\).

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Answer:

\(1352\)