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Discrete Math

Combination Calculator (nCr)

C(n, r) = n! / (r!(n−r)!). Free online Combination Calculator (nCr). Calculate combination calculator (ncr) online — fast, accurate, mobile-friendly, no signup

nCr
120

Derivation

  1. ├── 01Givenn = 10, r = 3
  2. ├── 02Formulat};return n(t) / (n(a) × n(t-a))
  3. ├── 03Substitutet};return 10(t) / (10(a) × 10(t-a))
  4. └── 04Compute nCr120
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§01What is

Understanding the Combination Calculator (nCr)

The Combination Calculator (nCr) computes nCr from 2 inputs: n, r. C(n, r) = n! / (r!(n−r)!).

Quick calculators for the math that shouldn’t need a notepad — instant, accurate, private to your browser. The Combination Calculator (nCr) sits in that toolkit — it C(n, r) = n! / (r!(n−r)!). Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

t};return n(t) / (n(a) × n(t-a))

Where

n
n
r
r
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: n = 10, r = 3.

  1. 01Start by noting the input — n: 10.
  2. 02Start by noting the input — r: 3.
  3. 03Substitute these values into the formula: t};return n(t) / (n(a) × n(t-a))
  4. 04Compute nCr: the calculator returns 120.
  5. 05Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Combination Calculator (nCr) Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

n halved

n = 5 (from 10)

Keep every other input at its default and halve the n. See how ncr responds.

  1. 01New n: 5
  2. 02Baseline nCr: 120
  3. 03New nCr: 10
  4. 04nCr decreases by 91.7% → use this sensitivity to plan for real-world variation.
02 · PATTERN

n doubled

n = 20 (from 10)

Keep every other input at its default and double the n. See how ncr responds.

  1. 01New n: 20
  2. 02Baseline nCr: 120
  3. 03New nCr: 1140
  4. 04nCr increases by 850% → use this sensitivity to plan for real-world variation.
03 · PATTERN

r halved

r = 1.5 (from 3)

Keep every other input at its default and halve the r. See how ncr responds.

  1. 01New r: 1.5
  2. 02Baseline nCr: 120
  3. 03New nCr: 90
  4. 04nCr decreases by 25% → use this sensitivity to plan for real-world variation.
04 · PATTERN

r doubled

r = 6 (from 3)

Keep every other input at its default and double the r. See how ncr responds.

  1. 01New r: 6
  2. 02Baseline nCr: 120
  3. 03New nCr: 210
  4. 04nCr increases by 75% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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