Convertools

Combinations (n choose r) Reference Values

Calculate the number of combinations using nCr for integers with 0 ≤ r ≤ n ≤ 18.

Author

Dr. Mateo Silva Herrera

Math editorial contributor

Colombian urban planner with a PhD from UCL, designing resilient infrastructure for flood-prone cities

Reviewed for accuracy by

Dr. Isabella Rossi

Math content reviewer

Italian neuroscientist at Sapienza University of Rome, studying the neural mechanisms of bilingual language processing

Last updatedFebruary 22, 2026

PublishedFebruary 22, 2026

Table of Contents

  1. All value pages
  2. Reference table
  3. FAQs
  4. Methodology and review
  5. Related conversions

Reference Value Index

This page lists 84 reference values for quick browsing and lookup.

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All Reference Values

Reference Table

Combinations (n choose r) reference values
ScenarionCr
3 n n; 0 r r1 Combination Count
3 n n; 1 r r3 Combination Count
3 n n; 2 r r3 Combination Count
3 n n; 3 r r1 Combination Count
4 n n; 0 r r1 Combination Count
4 n n; 1 r r4 Combination Count
4 n n; 2 r r6 Combination Count
4 n n; 3 r r4 Combination Count
4 n n; 4 r r1 Combination Count
5 n n; 0 r r1 Combination Count
5 n n; 1 r r5 Combination Count
5 n n; 2 r r10 Combination Count
5 n n; 3 r r10 Combination Count
5 n n; 4 r r5 Combination Count
5 n n; 5 r r1 Combination Count
6 n n; 0 r r1 Combination Count
6 n n; 1 r r6 Combination Count
6 n n; 2 r r15 Combination Count
6 n n; 3 r r20 Combination Count
6 n n; 4 r r15 Combination Count
6 n n; 5 r r6 Combination Count
6 n n; 6 r r1 Combination Count
7 n n; 0 r r1 Combination Count
7 n n; 1 r r7 Combination Count
7 n n; 2 r r21 Combination Count
7 n n; 3 r r35 Combination Count
7 n n; 4 r r35 Combination Count
7 n n; 5 r r21 Combination Count
7 n n; 6 r r7 Combination Count
7 n n; 7 r r1 Combination Count
8 n n; 0 r r1 Combination Count
8 n n; 1 r r8 Combination Count
8 n n; 2 r r28 Combination Count
8 n n; 3 r r56 Combination Count
8 n n; 4 r r70 Combination Count
8 n n; 5 r r56 Combination Count
8 n n; 6 r r28 Combination Count
8 n n; 7 r r8 Combination Count
8 n n; 8 r r1 Combination Count
9 n n; 0 r r1 Combination Count
9 n n; 1 r r9 Combination Count
9 n n; 2 r r36 Combination Count
9 n n; 3 r r84 Combination Count
9 n n; 4 r r126 Combination Count
9 n n; 5 r r126 Combination Count
9 n n; 6 r r84 Combination Count
9 n n; 8 r r9 Combination Count
9 n n; 9 r r1 Combination Count
10 n n; 0 r r1 Combination Count
10 n n; 1 r r10 Combination Count
10 n n; 2 r r45 Combination Count
10 n n; 3 r r120 Combination Count
10 n n; 4 r r210 Combination Count
10 n n; 5 r r252 Combination Count
10 n n; 6 r r210 Combination Count
10 n n; 9 r r10 Combination Count
10 n n; 10 r r1 Combination Count
12 n n; 0 r r1 Combination Count
12 n n; 1 r r12 Combination Count
12 n n; 2 r r66 Combination Count
12 n n; 3 r r220 Combination Count
12 n n; 4 r r495 Combination Count
12 n n; 5 r r792 Combination Count
12 n n; 6 r r924 Combination Count
12 n n; 11 r r12 Combination Count
12 n n; 12 r r1 Combination Count
15 n n; 0 r r1 Combination Count
15 n n; 1 r r15 Combination Count
15 n n; 2 r r105 Combination Count
15 n n; 3 r r455 Combination Count
15 n n; 4 r r1,365 Combination Count
15 n n; 5 r r3,003 Combination Count
15 n n; 6 r r5,005 Combination Count
15 n n; 14 r r15 Combination Count
15 n n; 15 r r1 Combination Count
18 n n; 0 r r1 Combination Count
18 n n; 1 r r18 Combination Count
18 n n; 2 r r153 Combination Count
18 n n; 3 r r816 Combination Count
18 n n; 4 r r3,060 Combination Count
18 n n; 5 r r8,568 Combination Count
18 n n; 6 r r18,564 Combination Count
18 n n; 17 r r18 Combination Count
18 n n; 18 r r1 Combination Count

Frequently Asked Questions

Frequently asked questions for Combinations (n choose r) and its reference values.

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

Each row on this page links to a value detail page derived from the same conversion data file as the main calculator and reference table. This reduces inconsistencies across page variants.

Editorial metadata and structured data are rendered across the converter page and linked value pages. Review policies are documented in our review process and editorial policy.