Program to calculate value of nCr

Following are common definition of Binomial Coefficients.

A binomial coefficient C(n, k) can be defined as the coefficient of X^k in the expansion of (1 + X)^n.
A binomial coefficient C(n, k) also gives the number of ways, disregarding order, that k objects can be chosen from among n objects; more formally, the number of k-element subsets (or k-combinations) of an n-element set.

Given two numbers n and r, find value of ⁿC_r

Examples :

Input :  n = 5, r = 2
Output : 10
The value of 5C2 is 10

Input : n = 3, r = 1
Output : 3

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

The idea is simply based on below formula.

ⁿC_r = (n!) / (r! * (n-r)!)

C++

// CPP program To calculate The Value Of nCr 
#include <bits/stdc++.h> 
using namespace std; 
  
int fact(int n); 
  
int nCr(int n, int r) 
{ 
    return fact(n) / (fact(r) * fact(n - r)); 
} 
  
// Returns factorial of n 
int fact(int n) 
{ 
    int res = 1; 
    for (int i = 2; i <= n; i++) 
        res = res * i; 
    return res; 
} 
  
// Driver code 
int main() 
{ 
    int n = 5, r = 3; 
    cout << nCr(n, r); 
    return 0; 
} 

Java

// Java program To calculate  
// The Value Of nCr 
class GFG { 
  
static int nCr(int n, int r) 
{ 
    return fact(n) / (fact(r) * 
                  fact(n - r)); 
} 
  
// Returns factorial of n 
static int fact(int n) 
{ 
    int res = 1; 
    for (int i = 2; i <= n; i++) 
        res = res * i; 
    return res; 
} 
  
// Driver code 
public static void main(String[] args) 
{ 
    int n = 5, r = 3; 
    System.out.println(nCr(n, r)); 
} 
} 
  
// This code is Contributed by 
// Smitha Dinesh Semwal. 

Python 3

# Python 3 program To calculate  
# The Value Of nCr 
  
def nCr(n, r): 
  
    return (fact(n) / (fact(r)  
                * fact(n - r))) 
  
# Returns factorial of n 
def fact(n): 
  
    res = 1
      
    for i in range(2, n+1): 
        res = res * i 
          
    return res 
  
# Driver code 
n = 5
r = 3
print(int(nCr(n, r))) 
  
# This code is contributed 
# by Smitha 

C#

// C# program To calculate  
// The Value Of nCr 
using System; 
  
class GFG { 
  
static int nCr(int n, int r) 
{ 
   return fact(n) / (fact(r) * 
                 fact(n - r)); 
} 
  
// Returns factorial of n 
static int fact(int n) 
{ 
    int res = 1; 
    for (int i = 2; i <= n; i++) 
        res = res * i; 
    return res; 
} 
  
   // Driver code 
   public static void Main() 
   { 
      int n = 5, r = 3; 
      Console.Write(nCr(n, r)); 
   } 
} 
  
// This code is Contributed by nitin mittal. 

PHP

<?php 
// PHP program To calculate 
// the Value Of nCr 
  
  
function nCr( $n, $r) 
{ 
    return fact($n) / (fact($r) *  
                  fact($n - $r)); 
} 
  
// Returns factorial of n 
function fact( $n) 
{ 
    $res = 1; 
    for ( $i = 2; $i <= $n; $i++) 
        $res = $res * $i; 
    return $res; 
} 
  
    // Driver code 
    $n = 5; 
    $r = 3; 
    echo nCr($n, $r); 
      
// This code is contributed by vt_m. 
?> 

Output:

More Efficient Solutions:
Dynamic Programming | Set 9 (Binomial Coefficient)
Space and time efficient Binomial Coefficient

All Articles on Binomial Coefficient

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My Personal Notes

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python 3

C#

PHP

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