Program to print the combination (nCr) of the given number

Program to print the combination (nCr) of the given number on fibonacci, factorial, prime, armstrong, swap, reverse, search, sort, stack, queue, array, linkedlist, tree, graph, pattern, string etc.

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Program to print the combination (nCr) of the given number

Combination (nCr) can be defined as the combination of n things taken r at a time without any repetition.

ncr can be calculated as,

nCr = [n(n-1) ... (n-r+1)] / r(r-1)...1

Algorithm

MAIN

STEP 1: START
STEP 2: DEFINE n, r
STEP 3: ENTER n, r
STEP 4: PRINT nCr(n, r)
STEP 5: END

nCr(n r)

STEP 1: START
STEP 2: RETURN fact(n) / (fact(r)*fact (n-r))
STEP 3: END

fact(n)

STEP 1: START
STEP 2: SET res= 1
STEP 3: REPEAT STEP 3 and STEP 4 UNTIL i<=n
STEP 4: res = res*i
STEP 5: RETURN res
STEP 6: END

Java Program

import java.util.*;
class Combination { 
static int nCr(int n, int r) 
{ 
	return fact(n) / (fact(r) * 
	fact(n - r)); 
} 
static int fact(int n) 
{ 
	int res = 1; 
           for (int i = 2; i <= n; i++) 
           res = res * i; 
          return res; 
} 
public static void main(String[] args) 
{ 
int n,r;
System.out.println("Enter the value of n and r?");
Scanner sc = new Scanner(System.in);
n = sc.nextInt();
r = sc.nextInt();
System.out.println("nCr = "+nCr(n, r));
} 
}

Output:

Enter the value of n and r?
6
4
nCr = 15

C Program

#include <stdio.h>
int fact(int z);
void main()
{
    int n, r, nCr;
    printf("Enter the value of n and r?");
    scanf("%d %d",&n,&r);
    nCr = fact(n) / (fact(r) * fact(n - r));
    printf("\nnCr = %d", nCr);
}

int fact(int z)
{
    int f = 1, i;
    if (z == 0)
    {
        return(f);
    }
    else
    {
        for (i = 1; i <= z; i++)
	{
            f = f * i;
	}
    }
    return(f);
}

Output:

Enter the value of n and r? 5  3
nCr = 10

Python Program

def fact(z):
    f = 1
    if z == 0:
        return f;
    else:
        for i in range(1,z+1):
            f = f * i;
        return f;


n=int(input("Enter the value of n"))
r = int(input("Enter the value of r"))
nCr = fact(n) / (fact(r) * fact(n - r));
print("\nnCr = %d" %(nCr));

Output:

Enter the value of n 5
Enter the value of r 3
nCr = 10

C# Program

using System; 
class Combination
{
static int nCr(int n, int r) 
{ 
   return fact(n) / (fact(r) * 
     fact(n - r)); 
} 
  static int fact(int n) 
{ 
  int res = 1; 
  for (int i = 2; i <= n; i++) 
   res = res * i; 
  return res; 
} 
   public static void Main() 
 { 
   int n,r;
   Console.WriteLine("Enter the value of n and r?");
   n = Convert.ToInt32(Console.ReadLine());
   r = Convert.ToInt32(Console.ReadLine());
   Console.Write("nCr = "+nCr(n, r)); 
 } 
}

Output:

Enter the value of n and r? 5 3  
nCr = 10

PHP Program

<?php 
function nCr( $n, $r) 
{ 
  return fact($n) / (fact($r) *  fact($n - $r)); 
} 
function fact( $n) 
{ 
 $res = 1; 
  for ( $i = 2; $i <= $n; $i++) 
  $res = $res * $i; 
  return $res; 
} 
 echo "Enter the value of n and r?";
 $n = readline(); 
 $r = readline(); 
  echo "ncr = ";
  echo nCr($n, $r); 
?>

Output:

Enter the value of n and r? 5 3  
nCr = 10

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Program to print the combination (nCr) of the given number