11.1 Counting Techniques

A selection of items from a larger set where the order does not matter.

An arrangement of items from a larger set where the order does matter.

C(n, r) = n! / (r!(n - r)!) where n is the total number of items and r is the number of items to choose.

P(n, r) = n! / (n - r)! where n is the total number of items and r is the number of items to arrange.

If one event can occur in m ways and a second can occur independently in n ways, then the two events can occur in m × n ways.

680

12

The number of ways to arrange 2 items from a set of 7, which equals 42.

192

A permutation considers the order of selection, while a combination does not.