Combinatronics

It’s easier in R if we look at these backwards.

Combinations

• Order doesn’t matter, so (1, 2) == (2, 1)
• \(\frac{n!}{k!(n-k)!}={n \choose k}\)
• choose(n, k)
• combn(x, m) to generate matrix of combinations

Permutations

• Cares about order (so there are more)
• \(\frac{n!}{(n-k)!}={n \choose k}\cdot k!\)
• choose(n, k) * factorial(k)
• prod(n - (0:(k - 1))) = more efficient