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How many different 5-letter “words” (sequences) are there with no repeated letters formed from the 26-letter alphabet

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    I'm gonna start putting a penny into a jar every time someone asks this, if anyone has a problem with this he will be able to find me in my private island. – 2017-01-01

3 Answers 3

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HINT: How many options are there for the first letter? After you used one letter how many for the second?

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Hint:

Consider $5$ slots to fill in the letters.

In the first box, there are $26$ options.

In the second box, there are $26-1$ options, as we cannot repeat the previous letter.

Do similar stuff for third, fourth and fifth box.

Multiply them up.

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Its P(26,5).

= $\frac{26!}{21!}$

= $\frac{26 \times 25 \times 24 \times 23 \times 22 \times 21!}{21!}$

So you have $26 \times 25 \times 24 \times 23 \times 22$ as a answer.

Edit -

You are picking first letter you have 26 options. After picking first letter you have 25 option to pick second letter. So on for picking 5 letters.

Then you have $26 \times 25 \times 24 \times 23 \times 22$ as a answer.