# How many three letter arrangements of the word ALGORA are there?

##### 1 Answer

72 arrangements

#### Explanation:

This is a permutation question in that we care about the order of the letters. The general formula is:

If all the letters were different, we'd have:

However, we have to deal with the repeated A.

Unfortunately, we can't simply divide by

**At most one A**

That's 5 distinct letters and we're selecting 3 of them:

**Both As**

There are 4 letters that are not A and it can be placed in any one of 3 places (first letter, second, or third). That gives:

We now add these results: