🎓 Mathematics • Probability
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Combination Calculator (nCr)
Computes combinations C(n, r) for subsets where the order of selection does not matter.
Permutations (nPr) & Combinations (nCr)
Calculate arrangements where order matters (Permutations) and groupings where order does not matter (Combinations).
Presets:
P / C
Permutations: P(7, 3) [Order Matters]
210
nPr = 7! / (7 − 3)! = 7! / 4! = 210
Combinations: C(7, 3) [Order Irrelevant]
35
nCr = 7! / [3! × (7 − 3)!] = 7! / [3! × 4!] = 35
What is a Combination?
A combination is a selection of items from a larger pool where the order of choice does not matter (e.g. lottery numbers, hands of cards).
Formula & Step-by-Step Calculation
nCr = (n choose r) = n! / [r! (n - r)!]
Binomial coefficient formula dividing out permutations of the subset.
Worked Step-by-Step Examples
Example 1
Choose a committee of 3 from 7 people
Solution: 35
• 7C3 = 7! / (3! × 4!) = (7 × 6 × 5) / 6 = 35
Common Real-World & Academic Use Cases
- ✓ Poker card hand probabilities
- ✓ Lottery ticket combinations
- ✓ Team squad selections
How to Use the Combination Calculator (nCr)
1
Input n & r
Input pool size n and selection size r.
2
View Combinations
Read total unique combinations.
Frequently Asked Questions
Q: Is nCr symmetric?
Yes, nCr = nC(n - r) because choosing r items leaves (n - r) items.