Permutations/Combinations/Counting Principle

A permutation is an arrangement of objects in a specific order. The order matters.

A combination is a selection of objects where the order does not matter.

The 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.

The formula is P(n, r) = n! / (n - r)!.

The formula is C(n, r) = n! / [r!(n - r)!].

A factorial, denoted as n!, is the product of all positive integers up to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.

There are 3! = 6 ways to arrange 3 books.

You can make C(5, 2) = 10 combinations.

Permutations consider the order of selection, while combinations do not.

There are P(10, 2) = 90 ways to choose a president and a vice president.