Combinations (n choose r)
Calculate the number of combinations using nCr for integers with 0 ≤ r ≤ n ≤ 18.
Table of Contents
9 n n; 3 r r =
84 Combination Count
Representative value from the Combinations (n choose r) reference table.
Reference Values
Browse 84 reference values with individual detail pages for quick lookup.
Combinations (n choose r)
Calculate the number of combinations using nCr for integers with 0 ≤ r ≤ n ≤ 18.
Calculated Result
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Reference Table
Use this complete table for quick lookup and internal linking to specific value pages.
| Scenario | nCr |
|---|---|
| 3 n n; 0 r r | 1 Combination Count |
| 3 n n; 1 r r | 3 Combination Count |
| 3 n n; 2 r r | 3 Combination Count |
| 3 n n; 3 r r | 1 Combination Count |
| 4 n n; 0 r r | 1 Combination Count |
| 4 n n; 1 r r | 4 Combination Count |
| 4 n n; 2 r r | 6 Combination Count |
| 4 n n; 3 r r | 4 Combination Count |
| 4 n n; 4 r r | 1 Combination Count |
| 5 n n; 0 r r | 1 Combination Count |
| 5 n n; 1 r r | 5 Combination Count |
| 5 n n; 2 r r | 10 Combination Count |
| 5 n n; 3 r r | 10 Combination Count |
| 5 n n; 4 r r | 5 Combination Count |
| 5 n n; 5 r r | 1 Combination Count |
| 6 n n; 0 r r | 1 Combination Count |
| 6 n n; 1 r r | 6 Combination Count |
| 6 n n; 2 r r | 15 Combination Count |
| 6 n n; 3 r r | 20 Combination Count |
| 6 n n; 4 r r | 15 Combination Count |
| 6 n n; 5 r r | 6 Combination Count |
| 6 n n; 6 r r | 1 Combination Count |
| 7 n n; 0 r r | 1 Combination Count |
| 7 n n; 1 r r | 7 Combination Count |
| 7 n n; 2 r r | 21 Combination Count |
| 7 n n; 3 r r | 35 Combination Count |
| 7 n n; 4 r r | 35 Combination Count |
| 7 n n; 5 r r | 21 Combination Count |
| 7 n n; 6 r r | 7 Combination Count |
| 7 n n; 7 r r | 1 Combination Count |
| 8 n n; 0 r r | 1 Combination Count |
| 8 n n; 1 r r | 8 Combination Count |
| 8 n n; 2 r r | 28 Combination Count |
| 8 n n; 3 r r | 56 Combination Count |
| 8 n n; 4 r r | 70 Combination Count |
| 8 n n; 5 r r | 56 Combination Count |
| 8 n n; 6 r r | 28 Combination Count |
| 8 n n; 7 r r | 8 Combination Count |
| 8 n n; 8 r r | 1 Combination Count |
| 9 n n; 0 r r | 1 Combination Count |
| 9 n n; 1 r r | 9 Combination Count |
| 9 n n; 2 r r | 36 Combination Count |
| 9 n n; 3 r r | 84 Combination Count |
| 9 n n; 4 r r | 126 Combination Count |
| 9 n n; 5 r r | 126 Combination Count |
| 9 n n; 6 r r | 84 Combination Count |
| 9 n n; 8 r r | 9 Combination Count |
| 9 n n; 9 r r | 1 Combination Count |
| 10 n n; 0 r r | 1 Combination Count |
| 10 n n; 1 r r | 10 Combination Count |
| 10 n n; 2 r r | 45 Combination Count |
| 10 n n; 3 r r | 120 Combination Count |
| 10 n n; 4 r r | 210 Combination Count |
| 10 n n; 5 r r | 252 Combination Count |
| 10 n n; 6 r r | 210 Combination Count |
| 10 n n; 9 r r | 10 Combination Count |
| 10 n n; 10 r r | 1 Combination Count |
| 12 n n; 0 r r | 1 Combination Count |
| 12 n n; 1 r r | 12 Combination Count |
| 12 n n; 2 r r | 66 Combination Count |
| 12 n n; 3 r r | 220 Combination Count |
| 12 n n; 4 r r | 495 Combination Count |
| 12 n n; 5 r r | 792 Combination Count |
| 12 n n; 6 r r | 924 Combination Count |
| 12 n n; 11 r r | 12 Combination Count |
| 12 n n; 12 r r | 1 Combination Count |
| 15 n n; 0 r r | 1 Combination Count |
| 15 n n; 1 r r | 15 Combination Count |
| 15 n n; 2 r r | 105 Combination Count |
| 15 n n; 3 r r | 455 Combination Count |
| 15 n n; 4 r r | 1,365 Combination Count |
| 15 n n; 5 r r | 3,003 Combination Count |
| 15 n n; 6 r r | 5,005 Combination Count |
| 15 n n; 14 r r | 15 Combination Count |
| 15 n n; 15 r r | 1 Combination Count |
| 18 n n; 0 r r | 1 Combination Count |
| 18 n n; 1 r r | 18 Combination Count |
| 18 n n; 2 r r | 153 Combination Count |
| 18 n n; 3 r r | 816 Combination Count |
| 18 n n; 4 r r | 3,060 Combination Count |
| 18 n n; 5 r r | 8,568 Combination Count |
| 18 n n; 6 r r | 18,564 Combination Count |
| 18 n n; 17 r r | 18 Combination Count |
| 18 n n; 18 r r | 1 Combination Count |
Frequently Asked Questions
Common questions about Combinations (n choose r), formulas, and typical use cases.
What does the Combinations (n choose r) calculator do?
It helps with counting selections where order does not matter in combinatorics and probability.
What formula does the Combinations (n choose r) calculator use?
nCr = n! / (r!(n-r)!), computed iteratively for stable exact integer results in range.
What inputs are valid?
n and r must be integers with 0 ≤ r ≤ n ≤ 18.
When would I use this?
counting selections where order does not matter in combinatorics and probability
Methodology and Review
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