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Let's say we have a $n$ letter word, and we want to find the number of possible anagrams.

For example, "cat" would have $6$ possible anagrams, because:

"cat", "cta", "act", "atc", "tac", "tca" are the possible rearrangements.

Another example would be a four-letter word, let us say "ABCD".

Then for anagrams that start off with "A", we have 6 anagrams:

"ABCD", "ABDC", "ACBD", "ACDB", "ADBC", "ADCB"

And we would multiply by $4$ to get the total anagram, implying there are $24$ possible anagrams for a four-letter word.

If there is a $20$-letter word, how many anagrams would there be?

Right now what I can think of is $n!$ anagrams for an $n$-letter word but am I correct, or am I missing something?

K.Hu.1106
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1 Answers1

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If all the $n$ letters differ, then there are indeed $n!$ permutations of the letters.

David G. Stork
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