Permutations

A permutation of \( n \) distinct objects is an ordered arrangement of these objects.

The number of permutations is the factorial: \( n! = n \times (n-1) \times \cdots \times 3 \times 2 \times 1 \) (

$n! = n \times (n-1) \times \cdots \times 3 \times 2 \times 1$

).

Examples:

• There are \( 4! = 24 \) ways to arrange $4$ different books on a shelf.
• There are \( 5! = 120 \) ways to assign $5$ different tasks to $5$ employees.

In permutations, the order of all the objects matters very much.

If order of all or some of the objects does not matter to us, we must use combinations instead, as we do on the next slide.