How many 5-letter words can we make if the letters are in order?

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Using the $26$ English letters, the number of $5$-letter words that can be made if the letters are distinct is determined as follows:

$26P5=26\times25\times24\times23\times22=7893600$ different words.

What if the letters in each word are in alphabetical order?

For example, the word JLOQY is valid, but the word JUMPY is invalid since U can not be before M

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3 Answers

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Hint. How many ways can you choose the five different letters? Once you have them, in how many ways can you organize them in alphabetical order?

(This assumes the letters are distinct.)

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Divide out the number of permutations of five letters ($5!$), since only one is correct.

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The different number of ways to select 5 alphabets from 26 alphabets= $26C5$.

Arrange the alphabets each collection in the required order.

Thus the answer is $26C5$.

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