Question

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

Answer 1

`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.