Problem

How many different arrangements of 5 letters can be formed if the first letter must be $W$ or $K$ (repeats of letters are allowed)? There are different 5 -letter combinations that can be formed. (Simplify your answer.)

Solution

Step 1 :The problem is asking for the number of different arrangements of 5 letters that can be formed if the first letter must be either 'W' or 'K'. Repeats of letters are allowed.

Step 2 :For the first letter, there are 2 choices: 'W' or 'K'.

Step 3 :For the remaining 4 letters, there are no restrictions, so each of them can be any of the 26 letters in the alphabet.

Step 4 :Therefore, the total number of arrangements can be calculated as \(2 * 26^4\).

Step 5 :Using Python to simplify the expression, we find that \(2 * 26^4 = 913952\).

Step 6 :So, the total number of different arrangements of 5 letters that can be formed if the first letter must be 'W' or 'K' is \(\boxed{913952}\).

From Solvely APP
Source: https://solvelyapp.com/problems/29357/

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