Permutations – Ordered Selections

A permutation counts the number of ways to choose and arrange r items from a set of n distinct items, where order matters. The formula is nPr = n × (n − 1) × … × (n − r + 1) – exactly r factors, counting down from n.

The key clue that a problem needs permutations, not combinations, is whether swapping the order of the chosen items creates a genuinely different outcome – like awarding 1st and 2nd place, where giving gold to Alex and silver to Sam is different from the reverse.

The Permutation Formula

Real-Life Application

• Race results: counting the ways to award 1st, 2nd, and 3rd place.
• Passwords: counting ordered arrangements of a fixed set of characters.
• Scheduling: counting the ways to order a set of tasks or events.

Key Takeaways

Practice: Permutations