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  • What is the number of ways we can choose three letters from $\{A,B,...,Z\}$ if repetition is allowed?

This is not a permutation.

Is there any formula to solve this kind of problems?

YuiTo Cheng
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user366312
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    Does order matter? Regardless of that, this set is so small that you can surely just write out all the possibilities. That might suggest a way to proceed in general. – lulu Jun 02 '18 at 09:27
  • Any ideas of your own. Let us share in it. We are here to learn ;-) – Vera Jun 02 '18 at 09:30

2 Answers2

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Yes, there is a formula. Apply it with $n=26$ and $k=3$.

Gibbs
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  • If you want a link to a very similar problem: https://math.stackexchange.com/questions/1723242/the-probability-that-a-candidate-comes-with-all-3-pens-having-the-same-colour?utm_medium=organic&utm_source=google_rich_qa&utm_campaign=google_rich_qa – Tony Hellmuth Jun 02 '18 at 10:11
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What is the number of ways we can choose three letters from {A,B,...,Z} if repetition is allowed?

English alphabet has 26 letters $\{A,B,C,...,Z\}$ and you want a string of length 3 so say we have 3 empty spots __ __ __

How to do it practically:

The first spot could have any of the $26$ letters, the second can have any of the $26$ letters, and finally the third will have any of the $26$ letters. Therefore, you have $26*26*26$ which is equal to $26^3$ since the repetition is allowed.

If elements are not to be repeated so you have $26$ different possibilities for the first slot, $25$ for the second since $1$ was used in the first, and finally, $24$ left for the last one which would give $26*25*24$ which would be permutations without repetition and with order, which is $26P3$

if the order doesn't matter and repetition is not allowed ${26 \choose 3}$

And for the formula, it is what Gibbs said.

Mr Pro Pop
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