# C program to find the value of nCr for a given value of n & r

In this C Programming example, we will implement the program to find the value of nCr for a given value of n & r and print the output on the console.

## 1. What is nCr in Probability – Mathematics?

`nCr` is a probability function that represents combination, it states the selection of ‘r‘ elements from a group or set of ‘n‘ elements, such that the order of elements does not matter. The formula to find combinations of elements is-

```nCr = n!/(r! * (n-r)!)
Here,
n = the total number of items or net size.
r = It is the subnet size or total number of items chosen from sample. ```
```Example:
Input
n: 8
r: 4

Formula
8!/(4! * (8−4)!)
= 8!/(4! * 4!)
= 40320/(24*24)
= 70

Output
4 C 3 is 70```

Helpful topics to understand this program better are-

## 2. C Program to find the value of nCr for a given value of n & r

Let’s discuss the execution(kind of pseudocode) for the program to find the value of nCr for a given value of n & r in C.

1. Initially, the program will prompt the user to enter the values of n and r.
2. Now, we invoke the function `int nCr(int n, int r)`, within this function, we call `int fact(int n)` function to calculate the required factorial values.
3. Factorial values are used to calculate the `nCr` value and then we print this value on the console.

In this C Programming example, we have discussed how to find the value of nCr for a given value of n & r in C.

```#include <stdio.h>
int fact(int n);

int nCr(int n, int r) { return fact(n) / (fact(r) * fact(n - r)); }

// This functions returns factorial of n
int fact(int n) {
int res = 1;
for (int i = 2; i <= n; i++) {
res = res * i;
}
return res;
}
int main() {
int n, r;
printf("Enter the value of n: ");
scanf("%d", &n);
printf("Enter the value of r: ");
scanf("%d", &r);

printf("The value of %dC%d is %d", n, r, nCr(n, r));
return 0;
}```

Note: Only whole positive integer numbers are valid.

```Output
Enter the value of n: 5
Enter the value of r: 4
The value of 5C4 is 5```

## 3. Conclusion

In this C Programming example, we have discussed how to find the value of nCr for a given value of n & r in C and discussed the steps of the program in detail.

Also for the example C programs please refer to C Programming Examples.

All examples are hosted on Github.

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Happy coding!! 😊

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