FCP, Combinations, and Permutations

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

A permutation is an arrangement of items from a larger set where the order does matter.

The Fundamental Counting Principle states that if one event can occur in 'm' ways and a second event can occur independently in 'n' ways, then the two events can occur in m × n ways.

Use combinations when the order of selection does not matter, such as choosing members for a committee.

Use permutations when the order of arrangement matters, such as assigning roles or positions.

This is a combination problem, calculated as C(165, 3).

This is a permutation problem, calculated as P(10, 3) = 720.

This is a combination problem, calculated as C(14, 5) = 2002.

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.