An ordered set is a set where the order of the elements matter. Without replacement means that you can’t pick the same element more than once.
Theory
When you draw elements from a set of elements, you call the number of possible orders the permutations.
Note! The order of the drawn elements matters!
Example 1
15 teams are joining a relay race.
That means there are 2730 different ways to fill the three first places when there are 15 teams.
Example 2
You’re electing 4 students for the student council from a group of 31 people: One president, one vice president, one secretary and one treasurer.
That means you can elect different student councils.