Basic Permutation Examples

Combinatorics · Axiom Academy

EXAMPLE Basic Permutation Examples Walk through fundamental permutation problems step-by-step Excellent work! You've completed these permutation examples. Here's what we learned: Full Permutations: When arranging n distinct objects in n positions, use n! . This applies to books on a shelf, people in chairs, or runners finishing a race. r-Permutations: When selecting and arranging r objects from n distinct objects, use P(n,r) = n!/(n-r)! . This accounts for choosing which objects to use AND their order. Order Matters: Permutations are used when the order of arrangement is important. If we're making "words" or assigning distinct prizes, different orders create different outcomes. The Multiplication Principle: Both formulas come from the multiplication principle: multiply the number of choices at each step (6×5×4×3×2×1 for 6 books, or 10×9×8 for 3 prizes from 10 people). These fundamental permutation formulas are the building blocks for more complex counting problems. Practice identifying when order matters versus when it doesn't!

This is the written version of the interactive lesson above. See the full Combinatorics course.