Math

Calculate Permutations and Combinations

Built by Kevin Glover · @gloverbuilds · Verified formula

Calculate nPr (permutations) and nCr (combinations). How many ways to arrange or choose from a group.

📅 Updated April 2026 ✅ Formula verified 📖 4 min read 🆓 Free · No sign-up

In this article

Permutations vs Combinations
When to Use Each

La Différence

Permutation : l'ordre compte. Combinaison : l'ordre ne compte pas. 3 personnes sur 10 pour des positions (président, VP, trésorier) : P(10,3) = 720. 3 personnes sur 10 pour un comité (sans rôle) : C(10,3) = 120. P est toujours ≥ C car il y a plus de façons d'arranger quand l'ordre compte.

Applications

Loterie (combinaison : l'ordre ne compte pas). Mots de passe (permutation : l'ordre compte). Planning d'équipes (combinaison). Podium (permutation).

⚡ CalcWolf Insight

The lottery is the most visible application of combinations. Powerball odds (1 in 292 million) mean: if you bought 100 tickets per week, you would expect to win once every 56,000 years. The expected value of a $2 Powerball ticket is about $0.85 — a 57% loss on every dollar played.

Frequently asked questions

Permutation ou combinaison ?▾

Si l'ordre importe (1er, 2e, 3e) : permutation. Si l'ordre ne compte pas (un groupe de 3) : combinaison.

Probabilité de la loterie ?▾

Loto français (5 parmi 49 + 1 parmi 10) : C(49,5) × 10 = 19 068 840 possibilités. 1 chance sur ~19 millions.

✓ Math logic verified against primary sources → See our verification process

Kevin Glover · @gloverbuilds

Founder, CalcWolf · GLVTS · Blickr

All formulas sourced from primary references — IRS publications, peer-reviewed research, and official standards. Results are tested against independent reference calculators before publishing. Rates and brackets updated when official sources change. Editorial policy →