- #1

Mr Davis 97

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- 44

## Homework Statement

How many strings of four lowercase letters have x in them?

## Homework Equations

## The Attempt at a Solution

It seems that there are two ways of doing this. First, there are four ways to choose where the x goes, and then there are 25^3 number of ways to choose what the other letters are. So in total there would be 4(25)^3 = 62500 ways.

But another valid way would be to count the complement. That is, there are 26^4 strings of four lowercase letters, and there are 25^4 strings of lowercase letters with no x. Thus 26^4 - 25^4 = 66351 would be how many lowercase letters have an x.

These two numbers obviously don't match. So what could I be doing wrong?