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nCr or C(n,r) Formula

GoNo of Combinations of N Different Things taken R at once Formula

GoNo of Combinations of N Different Things taken R at once and Repetition Allowed Formula

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Number of Combinations is defined as the total number of unique arrangements that can be made from a set of items, without regard to the order of the items. Check FAQs

C = \frac{n!}{r! \cdot (n - r)!}

C - Number of Combinations?n - Value of N?r - Value of R?

nCr or C(n,r) Example

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Here is how the nCr or C(n,r) equation looks like with Values.

Here is how the nCr or C(n,r) equation looks like with Units.

Here is how the nCr or C(n,r) equation looks like.

70 = \frac{8!}{4! \cdot (8 - 4)!}

70 = \frac{8!}{4! \cdot (8 - 4)!}

70 = \frac{8!}{4! \cdot (8 - 4)!}

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nCr or C(n,r) Solution

Follow our step by step solution on how to calculate nCr or C(n,r)?

FIRST Step Consider the formula

C = \frac{n!}{r! \cdot (n - r)!}

Next Step Substitute values of Variables

∴

C = \frac{8!}{4! \cdot (8 - 4)!}

Next Step Prepare to Evaluate

∴

C = \frac{8!}{4! \cdot (8 - 4)!}

LAST Step Evaluate

∴

C = 70

nCr or C(n,r) Formula Elements

Variables

Number of Combinations

Number of Combinations is defined as the total number of unique arrangements that can be made from a set of items, without regard to the order of the items.

Symbol: C

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Combinations

Value of N

Value of N is any natural number or positive integer that can be used for combinatorial calculations.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Value of N

Value of R

Value of R is the number of things that are selected for Permutation or Combination out of a given set of 'N' things, and it should be always less than n.

Symbol: r

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Value of R

Other Formulas to find Number of Combinations

Go No of Combinations of N Different Things taken R at once

C = C (n, r)

Go No of Combinations of N Different Things taken R at once and Repetition Allowed

C = C ((n + r - 1), r)

Go No of Combinations of N Different Things taken R at once given M Specific Things Always Occur

C = C (\begin{matrix} n - m \\ r - m \end{matrix})

Go No of Combinations of N Different Things taken R at once given M Specific Things Never Occur

C = C ((n - m), r)

Other formulas in Combinations category

Go Nth Catalan Number

C n = (\frac{1}{n + 1}) \cdot C (2 \cdot n, n)

How to Evaluate nCr or C(n,r)?

nCr or C(n,r) evaluator uses Number of Combinations = (Value of N!)/(Value of R!*(Value of N-Value of R)!) to evaluate the Number of Combinations, The nCr or C(n,r) formula is defined as the number of combinations of n different things taken r at a time. Number of Combinations is denoted by C symbol.

How to evaluate nCr or C(n,r) using this online evaluator? To use this online evaluator for nCr or C(n,r), enter Value of N (n) & Value of R (r) and hit the calculate button.

FAQs on nCr or C(n,r)

What is the formula to find nCr or C(n,r)?

The formula of nCr or C(n,r) is expressed as Number of Combinations = (Value of N!)/(Value of R!*(Value of N-Value of R)!). Here is an example- 56 = (8!)/(4!*(8-4)!).

How to calculate nCr or C(n,r)?

With Value of N (n) & Value of R (r) we can find nCr or C(n,r) using the formula - Number of Combinations = (Value of N!)/(Value of R!*(Value of N-Value of R)!).

What are the other ways to Calculate Number of Combinations?

Here are the different ways to Calculate Number of Combinations-

Number of Combinations=C(Value of N,Value of R)
Number of Combinations=C((Value of N+Value of R-1),Value of R)
Number of Combinations=C((Value of N-Value of M),(Value of R-Value of M))

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nCr or C(n,r) Formula

​GoNo of Combinations of N Different Things taken R at once Formula

​GoNo of Combinations of N Different Things taken R at once and Repetition Allowed Formula

nCr or C(n,r) Example

nCr or C(n,r) Solution

nCr or C(n,r) Formula Elements

Other Formulas to find Number of Combinations

Other formulas in Combinations category

How to Evaluate nCr or C(n,r)?

FAQs on nCr or C(n,r)

Variable Name

GoNo of Combinations of N Different Things taken R at once Formula

GoNo of Combinations of N Different Things taken R at once and Repetition Allowed Formula