# How many ways can you arrange the letters in the word factor?

May 24, 2018

6! = 720 ways.

#### Explanation:

There are 6 choices for which letter goes first.
There are 5 choices left for which letter goes second.
There are 4 choices left for which letter goes third.
...
There is 1 choice left for which letter goes sixth.

The total number of ways to arrange all these letters in a row is thr product of all these numbers of choices.

$6 \times 5 \times 4 \times 3 \times 2 \times 1$
$= 720$

This number can also be written as 6!

### Note:

This works because all the letters in "factor" are unique. If there are duplicates, we would need to divide our answer by the number of duplicate words created due to each duplicated letter.