nCr or C(n,r) Calculator

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✖Value of N is any natural number or positive integer that can be used for combinatorial calculations.ⓘ Value of N [n]			+10% -10%
✖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.ⓘ Value of R [r]			+10% -10%

✖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.ⓘ nCr or C(n,r) [C]

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Formula

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nCr or C(n,r)

Formula

`"C" = ("n"!)/("r"!*("n"-"r")!)`

Example

`"70"=("8"!)/("4"!*("8"-"4")!)`

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nCr or C(n,r) Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of Combinations = (Value of N!)/(Value of R!*(Value of N-Value of R)!)
C = (n!)/(r!*(n-r)!)
This formula uses 3 Variables

Variables Used

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

STEP 1: Convert Input(s) to Base Unit

Value of N: 8 --> No Conversion Required
Value of R: 4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C = (n!)/(r!*(n-r)!) --> (8!)/(4!*(8-4)!)

Evaluating ... ...

C = 70

STEP 3: Convert Result to Output's Unit

70 --> No Conversion Required

FINAL ANSWER

70 <-- Number of Combinations

(Calculation completed in 00.004 seconds)

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Created by Divanshi Jain

Netaji Subhash University of Technology, Delhi (NSUT Delhi), Dwarka

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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

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< 14 Combinations Calculators

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

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

No of Combinations of (P+Q) Things into Two Groups of P and Q Things

Go Number of Combinations = ((Value of P+Value of Q)!)/((Value of P!)*(Value of Q!))

nCr or C(n,r)

Go Number of Combinations = (Value of N!)/(Value of R!*(Value of N-Value of R)!)

Nth Catalan Number

Go Nth Catalan Number = (1/(Value of N+1))*C(2*Value of N,Value of N)

No of Combinations of N Identical Things into R Different Groups if Empty Groups are Allowed

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

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

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

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

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

No of Combinations of N Different Things, P and Q Identical Things taken Atleast One at once

Go Number of Combinations = (Value of P+1)*(Value of Q+1)*(2^Value of N)-1

Maximum Value of nCr when N is Odd

Go Number of Combinations = C(Value of N (Odd),(Value of N (Odd)+1)/2)

No of Combinations of N Identical Things into R Different Groups if Empty Groups are Not Allowed

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

Maximum Value of nCr when N is Even

Go Number of Combinations = C(Value of N,Value of N/2)

No of Combinations of N Different Things taken R at once

Go Number of Combinations = C(Value of N,Value of R)

No of Combinations of N Different Things taken Atleast One at once

Go Number of Combinations = 2^(Value of N)-1

No of Combinations of N Identical Things taken Zero or more at once

Go Number of Combinations = Value of N+1

nCr or C(n,r) Formula

Number of Combinations = (Value of N!)/(Value of R!*(Value of N-Value of R)!)
C = (n!)/(r!*(n-r)!)

What are Combinations?

In combinatorics, Combinations refer to the different ways of selecting a subset of items from a larger set without regard to the order of selection. Combinations are used to count the number of possible outcomes when the order of selection does not matter. For example, if you have a set of three elements {A, B, C}, the Combinations of size 2 would be {AB, AC, BC}. In this case, the order of the items within each combination does not matter, so {AB} and {BA} are considered the same combination.

The number of Combinations of selecting "k" items from a set of "n" items is denoted as C(n, k). It is calculated using the binomial coefficient formula: C(n, k) = n! / (k! * (n - k)!)

Combinations have various applications in mathematics, probability theory, statistics, and other fields.

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

nCr or C(n,r) calculator uses Number of Combinations = (Value of N!)/(Value of R!*(Value of N-Value of R)!) to calculate 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 calculate nCr or C(n,r) using this online calculator? To use this online calculator for nCr or C(n,r), enter Value of N (n) & Value of R (r) and hit the calculate button. Here is how the nCr or C(n,r) calculation can be explained with given input values -> 56 = (8!)/(4!*(8-4)!).

FAQ

What is nCr or C(n,r)?

The nCr or C(n,r) formula is defined as the number of combinations of n different things taken r at a time and is represented as C = (n!)/(r!*(n-r)!) or Number of Combinations = (Value of N!)/(Value of R!*(Value of N-Value of R)!). Value of N is any natural number or positive integer that can be used for combinatorial calculations & 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.

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

The nCr or C(n,r) formula is defined as the number of combinations of n different things taken r at a time is calculated using Number of Combinations = (Value of N!)/(Value of R!*(Value of N-Value of R)!). To calculate nCr or C(n,r), you need Value of N (n) & Value of R (r). With our tool, you need to enter the respective value for Value of N & Value of R and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Number of Combinations?

In this formula, Number of Combinations uses Value of N & Value of R. We can use 12 other way(s) to calculate the same, which is/are as follows -

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))
Number of Combinations = C((Value of N-Value of M),Value of R)
Number of Combinations = 2^(Value of N)-1
Number of Combinations = Value of N+1
Number of Combinations = C(Value of N (Odd),(Value of N (Odd)+1)/2)
Number of Combinations = C(Value of N,Value of N/2)
Number of Combinations = (Value of P+1)*(Value of Q+1)*(2^Value of N)-1
Number of Combinations = ((Value of P+Value of Q)!)/((Value of P!)*(Value of Q!))
Number of Combinations = C(Value of N+Value of R-1,Value of R-1)
Number of Combinations = C(Value of N-1,Value of R-1)

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