Permutations and Combinations — Chapter Summary

If one event can occur

If one event can occur in 'm' ways and a second event can occur in 'n' ways after the first, then both events together can occur in m × n ways. This p

For a positive integer n

For a positive integer n, n! means the product of all positive integers from 1 to n. By convention, 0! = 1. For example, 4! = 4 × 3 × 2 × 1 = 24.

A permutation is an arrangement

A permutation is an arrangement of objects in a specific order. The number of ways to arrange r objects out of n is given by \( {}^n\mathrm{P}_r = \fr

A combination is a selection

A combination is a selection of objects where the order does not matter. The number of ways to choose r objects out of n is given by \( {}^n\mathrm{C}

When arranging n distinct objects

When arranging n distinct objects in a circle, the number of arrangements is (n-1)! because rotations are considered the same. If clockwise and anticl