Permutations can either be repetitions allowed or repetitions not allowed, as well as ordered or unordered. "With replacement" or "repetitions allowed" means the same thing as "identical trials." Examples include rolling dice, flipping coins, and drawing balls from a box with replacement. "Without replacement" or "repetitions not allowed" means the same thing as "depleting trials," or trials where the number of possible outcomes decreases by one after each trial. Examples include picking committees of people (because a given person cannot be repeated), assigning people to seats, and drawing balls from a box and not replacing them.

As far as "ordered versus disordered sets, ordered objects can be seen as viewed in a line, and disordered objects can be envisioned as an amorphous group. For example, an ordered committee is one where all of the members have given roles such as president or vice president, whereas an unordered committee is one where all roels are equal.

Calculations of the amount of potential permutations for a given set of objects will vary based on the ordering and replacement of the objects in a set. We will cover them all:

• Ordered sets, repetitions allowed
• Ordered sets, repetitions not allowed
• Unordered sets, repetitions not allowed
• Unordered sets, repetitions allowed