Recursive Function:

• A function that calls itself is called as recursive function.
• A recursive function must definitely have a condition that exists from calling the function again.
• Hence there must be a condition that calls the function itself if that condition is true.
• If the condition is false then it will exit from the loop of calling itself again.

Algorithm:

Main () Function:

• Start.
• Enter values of n and r to be printed”.
• Input n and r.
• Using formula of nCr = fact(n)/fact(n-r);
• C = CALL (k*fact(k-1));
• Print nCr.
• Stop.

Exponential (parameters: x, y)

• Start.
• If k=1, then return 1.
• Else return(kCALL (kfact(k-1)))
• Stop.

Program:

#include <stdio.h>
#include <conio.h>
int main(){
    int n, r, C;
    int fact(int k);
    printf("Enter the number n and r:");
    scanf("%d%d", &n, &r);

    C = fact(n)/fact(n-r);
    printf("nCr=%d\n", C);
    getch();
}
int fact(int k) {
    if(k==1)
    return 1;
    else
    return (k*fact(k-1));
}

Output:

Enter the number n and r = 5 3

$nC_r$ = 60

Explanation:

• In this program, to get value of nCr, we just divide fact(n) with fact(n-r).
• This is done by the recursive function “fact”.
• It checks the value of the index, if it is equal to 1, then it returns just the value 1.
• Else it passes the value of nCr by calling itself i.e. recursive function.