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.

Related questions
See all questions in Combinations and Permutations
Impact of this question
6109 views around the world
You can reuse this answer
Creative Commons License