- #1

Seda

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## Homework Statement

What is the probability of having at least two identical letters in a randomly selected string of four letters.

## Homework Equations

None, except maybe a basic idea of permutations/combinations

## The Attempt at a Solution

Well, probability seems like an easy topic, but I'm having trouble on this one.

First off, I'm assuming that the letters are picked simultaneously.

Well, I can see that obviously, the total number of possibilities is 26^4.

ANd I know I need to account for having 2 letters the same, 3 letters the same, and 4 letters the same.

Well, I know how to do this problem easy if I was given a specific letter to worry about. The result would be like this:

Probability = [25/26 X 25/ 25 X 1/26 X 1/26] + [25/26 X (1/26)^3] + [(1/26)^4]

---------------^2 the same -------------------------^ 3 the same ------ ^ all four the same

But this would only be the answer if I was given a specific letter to worry about being the same. How do I solve when it can be any letter?

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