Permutations, k-Permutations and Combinations
Number of Permutations[more]
The number of ways to arrange different objects in a row is . The exclamation mark "!" is read as "factorial". Of course, the product is the same in reverse order: . Each such arrangement is called a permutation. For consistency, it is assumed that .
Number of k-Permutations
If only of the objects are to be arranged in a row, the formula is
with factors. If , . Such an arrangement is called a partial permutation, or a -permutation. Clearly , because all objects are being arranged; the formula reduces to because the denominator is .
Number of Combinations
The number of ways to choose a subset of objects from objects is
Therefore, . Each choice of a subset is called a combination. Another notation for is . Again, if , . A special case is .[less]