How does the Combinations with Replacement work?

Unlike regular combinations, you can pick the same item multiple times Then: Order still does not matter (unlike permutations) Then: Formula: C(n+k-1, k) where n = types, k = selections Then: Example: Choosing 3 scoops from 5 ice cream flavors (can repeat) = C(7,3) = 35.

Can you give an example of how to use the Combinations with Replacement?

Example: Input n=5 flavors, k=3 scoops (repeats allowed) gives a result of C(7,3) = 35 combinations ((5+3-1)! / (3! × 4!) = 35).

Is the Combinations with Replacement free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Combinations with Replacement?

Our Combinations with Replacement uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

Matematică

Combinations with Replacement

Combinations Calculator

C(n,r) — order does not matter

n (total items)

r (items chosen)

Combinations with replacement (also called multiset coefficients) count the number of ways to choose k items from n types when you can repeat items and order does not matter. Formula: C(n+k-1, k) = (n+k-1)! / (k!(n-1)!)

Type	Formula	n=5, k=3
Without replacement	C(n,k) = n!/(k!(n-k)!)	C(5,3) = 10
With replacement	C(n+k-1,k)	C(7,3) = 35
Permutations without	P(n,k) = n!/(n-k)!	P(5,3) = 60
Permutations with	nᵏ	5³ = 125

💡

Pro Tip

Think of it as distributing k identical balls into n distinct bins: how many distributions are possible? The formula C(n+k-1, k) gives the answer.

⭐

Did You Know?

Combinations with replacement appear in number theory as 'stars and bars' problems, in physics for counting quantum states of identical particles (bosons), and in combinatorics textbooks as the 'ice cream flavor' problem.

References

›Combination — Wikipedia

🔒

100% Gratuit

Fără înregistrare

✓

Precis

Formule verificate

⚡

Instant

Rezultate în timp ce tastezi

📱

Mobile Ready

Toate dispozitivele

Combinations with Replacement

Combinations Calculator

Ce este Combinations with Replacement?

Cum să Combinations with Replacement

Exemple rezolvate

Combinations: With vs Without Replacement

Setări