Why do we divide Permutations to get to Combinations? I'm having a hard time reasoning through the formula for combinations $\frac{n!}{k!\left(n-k\right)!}$. I understand the reason for the permutations formula and I know that for the combinations we divide by $k!$ to adjust for the repeated cases, since order does not matter. But what exactly happens when we divide the set of permutations by $k!$ ? 
I know this may seem like a silly question... I just can't take this for granted, lest I miss a chance to apply it correctly. Can you describe what's happening here step by step, sort like debugging a script?

You divide by k! since that's the number of permutations for the k objects that you've taken. All the permutations/orders of each set of k objects is equivalent since you're dealing with combinations, so you have to divide that out.
