Need help understanding what method to tackle Perm/Comb ques

I have learned factorial and I can answer simple questions like how many 3-man group from 7 people.
But I become confused when it gets harder.

I must have missed the underlying fundamental concept I hope someone can shed some light.

Let's begin with very downright basic example, like:

Fill in 3 empty fields each with one of the following alphabets. How many unique combination? Order DOES matter?

Note: I don't just want the answer, I care more about how we go about tackling such question!

1) ABCDE
2) AABBCDE
3) AAABCCDDEEE