Program to calculate the value of nPr

• Difficulty Level : Easy
• Last Updated : 07 May, 2021

Given two numbers n and r, the task is to find the value of nPr.
nPr represents n permutation r which is calculated as n!/(n-k)!. Permutation refers to the process of arranging all the members of a given set to form a sequence. The number of permutations on a set of n elements is given by n! where “!” represents factorial.

nPr = n! / (n - r)!

Program:

C++

 // CPP program to calculate nPr#includeusing namespace std; int fact(int n){    if (n <= 1)        return 1;    return n * fact(n - 1);} int nPr(int n, int r){    return fact(n) / fact(n - r);} // Driver codeint main(){    int n = 5;    int r = 2;     cout << n << "P" << r << " = " << nPr(n, r);} // This code is contributed by// Surendra_Gangwar

Java

 // Java program to calculate nPr import java.util.*; public class GFG {     static int fact(int n)    {        if (n <= 1)            return 1;        return n * fact(n - 1);    }     static int nPr(int n, int r)    {        return fact(n) / fact(n - r);    }     public static void main(String args[])    {        int n = 5;        int r = 2;         System.out.println(n + "P" + r + " = "                           + nPr(n, r));    }}

Python3

 # Python3 program to calculate nPrimport mathdef fact(n):    if (n <= 1):        return 1             return n * fact(n - 1) def nPr(n, r):         return math.floor(fact(n) /                fact(n - r))     # Driver coden = 5r = 2 print(n, "P", r, "=", nPr(n, r)) # This code contributed by Rajput-Ji

C#

 // C# program to calculate nPrusing System; class GFG{     static int fact(int n)    {        if (n <= 1)            return 1;        return n * fact(n - 1);    }     static int nPr(int n, int r)    {        return fact(n) / fact(n - r);    }     public static void Main()    {        int n = 5;        int r = 2;         Console.WriteLine(n + "P" + r + " = "                        + nPr(n, r));    }} /* This code contributed by PrinciRaj1992 */



Javascript

 // Javascript program to calculate nPrfunction fact(n){    if (n <= 1)        return 1;             return n * fact(n - 1);} function nPr(n, r){    return Math.floor(fact(n) /                fact(n - r));}     // Driver codelet n = 5;let r = 2; document.write(n, "P", r, " = ", nPr(n, r)); // This code is contributed by gfgking
Output:
5P2 = 20

Optimization for multiple queries of nPr
If there are multiple queries for nPr, we may precompute factorial values and use the same for every call. This would avoid the computation of the same factorial values again and again.

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