Question

How many unique ways are there to arrange the letters in the word APE

Answer 1

Answer: 9

Step-by-step explanation:

Answer 2

Answer:

6

Step-by-step explanation:

So there are 2 ways to do this.

The first one is to actually just rearrange the letters as many ways as possible. So here's this method:

1. APE

2. AEP

3. PAE

4. PEA

5. EAP

6. EPA

So this method is fine when you just have 3 letters but once you get to more and more letters this becomes close to impossible to do. That's why we use the second method: factorials. When all of the letters in the word are different the equation is really simple. Since the word APE has 3 letters your equation will be 3!

[Mini lesson time!!!

What the happy little exclamation point does means is that you should take the number in front of it and multiply it by all of the numbers that come before it.]

So lets solve this now:

3!=x

1·2·3=x

6=x

(Once again... this method only works if all of the letters in the word are DIFFERENT. For example if you had the word FUNNEST, you would use a different equation because there are 2 of the letter 'N'.)

If anything I've said is confusing or you need any other help just let me know!!