# Combinations

“Order doesn’t matter”

Combinations = # of subsets of size $k$

Combinations are the same as Permutations, except order doesn’t matter.

- When the order DOESN’T matter, there are less number of permutations, which is why we have the extra $k!$ at the bottom.

We use the Binomial Coefficient to calculate the number of combinations.

Suppose we select $k$ slots from $n$ objects (where order **doesn’t** matter), the number of ways this can be done is (”$n$ choose $k$”):
$(kn )=(n−k)!k!n! =_{n}C_{k}$

#### Proof

We derive combinations from the idea that $_{n}C_{k}k!=_{n}P_{k}$

I am still having trouble understanding how to think about permutations.