# Combinations

Similar to but no regard to ordering.

As such we just select and treat selection as duplicates, since order of duplicates do not matter.

nPr / r!

## Binomial coefficient

nCr is binomial coefficient because it is coefficient of the term $$a^{r}b^{n - r}$$ in the binomial expansion of $$(a + b)^{n}$$.

It can be verified that the following hold:

1. nCr = nC(n - r) for r = 0,1,…,n
2. nCr = (n - 1)Cr + (n - 1)C(r - 1) for 1 <= r <= n
3. nCr = 0 for r < 0 or r > n