Mathematik

n Choose r Calculator

How Many Ways Can You Choose?

Type in the total number of items (n) and how many you want to pick (r), and this calculator instantly tells you how many different selections are possible. Perfect for homework problems, probability questions, and real-world counting problems like lottery odds or committee selection.

Beispiel ausprobieren

Wähle ein Szenario, um zu sehen, wie der Rechner funktioniert, und passe dann die Werte an

Lottoziehung

Berechne die Anzahl möglicher 6-aus-49-Kombinationen.

Wichtige Werte: Kugeln gesamt: 49 · Gezogen: 6 · Kombinationsmodus

Siegertreppchen

Finde heraus, auf wie viele Arten Gold, Silber und Bronze unter 8 Läufern vergeben werden können.

Wichtige Werte: Läufer: 8 · Medaillen: 3 · Permutationsmodus

Wichteln

Berechne gültige Geschenkzuweisungen, bei denen niemand seinen eigenen Namen zieht.

Wichtige Werte: Teilnehmer: 8 · Fixpunktfreie Permutation

Passwort-Schlüsselraum

Schätze die Anzahl möglicher 8-Zeichen-Passwörter aus druckbaren ASCII-Zeichen.

Wichtige Werte: Zeichensatz: 94 · Länge: 8 · Wiederholung erlaubt

Dokumentation

This calculator is also known as n Choose r Calculator.

Read the complete guide

Understanding "n Choose r"

"n choose r" is everyday language for the binomial coefficient C(n,r). It answers the question: how many ways can I select r items from a group of n?

Examples

Committee of 3 from 12

How many 3-person committees can be formed from 12 candidates?

C(12, 3) = 220 possible committees.

Key takeaway: Since committee members have no ranked roles, order does not matter.

Solving "How Many Ways" Problems

Approach counting problems systematically:

Identify n (total items) and r (items selected)
Determine whether order matters (permutation vs. combination)
Check whether repetition is allowed

Frequently Asked Questions about n Choose r Calculator

How do I know whether order matters?

Ask yourself: would rearranging my selection give a different outcome? If picking {A,B} is the same as {B,A}, use combinations (n choose r). If the order matters (like 1st vs 2nd place), use permutations.

What are C(n, 0) and C(n, n)?

Both equal 1. C(n,0) = 1 because there is exactly one way to select nothing. C(n,n) = 1 because there is only one way to select every item. These are the first and last entries in every row of Pascal's triangle.

Is "n choose r" the same as the binomial coefficient?

Yes. "n choose r" is another name for the binomial coefficient, written C(n,r) or ⁿCᵣ. It appears in Pascal's triangle and gives the coefficient of each term in the binomial theorem expansion of (a+b)^n.