Permutations & Combinations

Permutations

Number of permutations of size $k$ for a set of size $n$:

$$nPk = \frac{n!}{(n - k)!}$$

Combinations

Number of combinations of size $k$ for a set of size $n$:

$$nCk = \frac{n!}{k!(n - k)!} = \frac{nPk}{k!}$$

The number of combinations is always less than the number of permutations because order matters for permutations.