- Write a C program to find the value of nPr and nCr

**nPr** is the number of ways of obtaining an ordered subset of r elements from a set of n elements. Parameter n stands for the number of items in the complete set whereas r stands for the number of items you want to select. In other words, nPr means number of ways you can select r items from set of n items where order makes difference.

*nPr = n!/(n-r)!*
Where n!, denotes the factorial of a number, it is the product of all positive integers less than or equal to n. Factorial does not exist for negative numbers and factorial of 0 is 1. Its most basic occurrence is the fact that there are n! ways to arrange n distinct objects into a sequence. Hence, to calculate nPr, we have to calculate factorial of n and (n-r) and divides them as per above expression.

Before proceeding, I will recommend to check Factorial program first : Factorial Program in C

## C program to find nPr using function.

In this program we first take n and r as input form user. As per definition of **nPr**, n >= r. Which means, If a set contains n items then you cannot select more than n items from that set. Here we are using a user defined function getFactorial(N), which takes a number as input and return its factorial value. Function getNPR calls getFactorial function to calculate numerator and denominator or nPr expression.

/* * C Program to find nPr using function */ #include <stdio.h> #include <conio.h> int getFactorial(int N); int main(){ int n, r, nPr; printf("Enter n and r for nPr calculation\n"); scanf("%d %d",&n, &r); nPr = getNPR(n, r); if(nPr == -1){ printf("Invalid Input: n must be >= r\n"); } else { printf("%dP%d = %d\n", n, r, nPr); } getch(); return 0; } /* * Function to calculate nPr * nPr = n!/(n-r)! */ int getNPR(int n, int r){ if(r > n){ /* Invalid Input, n must be >= r */ return -1; } return getFactorial(n)/getFactorial(n - r); } /* * Function to calculate factorial of a number */ int getFactorial(int N){ if(N < 0){ printf("Invalid Input"); return 0; } int nFactorial, counter; /* N! = N*(N-1)*(N-2)*(N-3)*.....*3*2*1 */ for(counter = 1, nFactorial = 1; counter <= N; counter++){ nFactorial = nFactorial * counter; } return nFactorial; }

**Program Output**

Enter n and r for nPr calculation 6 2 6P2 = 30

## C program to find nCr using a function

**nCr** means number of ways you can select r items from set of n items where order makes no difference. It defines, IN how many ways we can select a small group from a larger group.

*For Example:*

In how many ways you can select a group of five employees from an office of 20 employees.

#### Points to Remember

- If the order doesn't matter, it is a
**Combination**. - If the order does matter it is a
**Permutation**.

*nCr = n!/(r!*(n-r)!)*

nCr = nPr/r!nCr = nPr/r!

**nPr**, then divide it with r! to get

**nCr**.

/* * C Program to find nCr using function */ #include <stdio.h> #include <conio.h> int getFactorial(int N); int main(){ int n, r, nCr; printf("Enter n and r for nCr calculation\n"); scanf("%d %d",&n, &r); nCr = getNCR(n, r); if(nCr == -1){ printf("Invalid Input: n must be >= r\n"); } else { printf("%dC%d = %d\n", n, r, nCr); } getch(); return 0; } /* * Function to calculate nPr * nCr = n!/r!*(n-r)! */ int getNCR(int n, int r){ if(r > n){ /* Invalid Input, n must be >= r */ return -1; } return getFactorial(n)/(getFactorial(r)*getFactorial(n - r)); } /* * Function to calculate factorial of a number */ int getFactorial(int N){ if(N < 0){ printf("Invalid Input"); return 0; } int nFactorial, counter; /* N! = N*(N-1)*(N-2)*(N-3)*.....*3*2*1 */ for(counter = 1, nFactorial = 1; counter <= N; counter++){ nFactorial = nFactorial * counter; } return nFactorial; }

**Program Output**

Enter n and r for nCr calculation 6 2 6C2 = 15

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