Question

how many different ways can you choose 3 vowels out of the box, if there are 5 vowels in the box and the order does NOT matter?
a. 10
b. 15
c. 30
d. 60

Answer 1

5 possibilities for the first choice. 4 possibilities for the second choice. 3 possibilities for the third choice.
5*4*3

Except, oh no! That means we're counting some possibilities more than once...
For example, here's one single outcome:
AEO
But, that could be written as
AEO, AOE, EAO, EOA, OAE, or OEA

So one choice can actually be written 6 different ways.

Answer 2

if all the vowels are different

Answer 3

If we just do 5*4*3, we're counting each actual choice 6 times.