Combinations
Similar to Permutations 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:
- nCr = nC(n - r) for r = 0,1,…,n
- nCr = (n - 1)Cr + (n - 1)C(r - 1) for 1 <= r <= n
- nCr = 0 for r < 0 or r > n
