How do you find the number of distinguishable permutations of the letters HONEST?

1 Answer
Alan P.
Jan 17, 2016

#6xx5xx4xx3xx2xx1=720#

Explanation:

Since all #6# letters in HONEST are distinct
there are #6# choices for the first letter;

Once a first letter has been chosen
there are #5# choices for the second letter;
so there are #6xx5 =30# choices for the permutations of the first and second letters.

Once the first and second letters have been chosen
there are #4# choices for the third letter;
so there are #6xx5xx4# choices for the permutations of the first three letters.

...and so on.

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