# Question #ff7fe

##### 1 Answer

We divided all

Below is the number of combinations and permutations in each group.

#### Explanation:

Let me interpret the problem in more details.

You would like to use all

You are asking how many different

I hope, that's what you meant.

If all letters in the initial word were different, we would have a textbook problem. Unfortunately, situation gets complicated since three letters, **A**, **I** and **N** are repeated twice.

Let's group all our

Group 1. No pairs of the same letters are present in a word.

Group 2. One pair of the same letters is present in a word.

Group 3. Two pairs of the same letters are present in a word.

There can be no more than two pairs present since the total number of letters in a word is

**Group 1**

There are *permutations* of

The number of *combinations* of

**Group 2**

There are three choices for a letter that is repeated twice, **A**, **I** and **N**. So, we have

With each of them we have *combinations* of

A pair of the same letters can be positioned in a *permutations* in this group is

**Group 3**

Our

The first pair of the same letters defines an entire permutation. We analyze the number of them for group 2, it's