Calculating Permutations and Combinations

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

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

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

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

The key difference is that permutations consider the order of selection, while combinations do not.

This is a permutation problem: P(10, 5) = 10! / (10 - 5)! = 30,240.

This is a combination problem: C(10, 3) = 10! / (3! * (10 - 3)!) = 120.

The factorial of a number n (denoted as n!) is the product of all positive integers up to n.

C(5, 2) = 5! / (2! * (5 - 2)!) = 10.

P(6, 4) = 6! / (6 - 4)! = 360.