Writing a Binomial Coefficient calculator in C : Problem with checking scanf failure

I want to write a computer programme that will do the following things :

1. Ask for two integer inputs n and k from the user using scanf.

2. If one of the scanfs don't return 1, it will print "Failed" and will return 1. or else it will do the following:

3. Calculate the Pochhammer symbol n_k. For example if n = 5 and k = 3 then

   poc = ( 5 - 0 ) * ( 5 - 1 ) * ( 5 - 2 ).

4. It will calculate the factorial k!. For example if k = 3 then

   fac = 1 * 2 * 3.

5. It will divide poc by fac and loop back to beginning.

I wrote the following which doesn't work:

#include <stdio.h>

unsigned long long bin_cof ( int bc_n , int bc_k ) {
    
    //calculate pochhammer symbol n_k
    int i = 0 ; unsigned long long poc = 1 ;
    for ( ; i < bc_k ; i++ ) { poc = poc * ( bc_n - i ) ; }
    
    //calculate factorial k! 
    i = 1 ; unsigned long long fac = 1 ;
    for ( ; i < bc_k ; i++ ) { fac = fac * ( i + 1 ) ; }

    //calculate binomial coefficient
    return poc / fac ;
}

int main (  ) {
    
    printf ( "Give me an n : " ) ; int n ; scanf ( "%d" , &n ) ;
    printf ( "Give me a k : " ) ; int k ; scanf ( "%d" , &k ) ;
    
    if ( scanf ( "%d" , &n ) != 1 ) { printf ( "!!Failed!!" ) ; return 1 ; }
    if ( scanf ( "%d" , &k ) != 1 ) { printf ( "!!Failed!!" ) ; return 1 ; }
    
    printf ( "\n%dC%d = %llu\n\n" , n , k , bin_cof ( n , k ) ) ; main (  ) ;

    return 0 ; 
}

But if I comment out the checking of the return value of scanfs part, it works.

    /*if ( scanf ( "%d" , &n ) != 1 ) { printf ( "!!Failed!!" ) ; return 1 ; }
    if ( scanf ( "%d" , &k ) != 1 ) { printf ( "!!Failed!!" ) ; return 1 ; }*/

What mistake/s am I making with checking the return values of scanfs and how can I correct it?

As noted in the good comments, you actually have some extra calls to scanf that you should not need to acquire your coefficient values. When I compiled your code, I received the following compiler warnings.

||=== Build: Release in Coefficient (compiler: GNU GCC Compiler) ===|
/home/craig/C_Programs/Console/Coefficient/main.c||In function ‘main’:|
/home/craig/C_Programs/Console/Coefficient/main.c|19|warning: ignoring return value of ‘scanf’ declared with attribute ‘warn_unused_result’ [-Wunused-result]|
/home/craig/C_Programs/Console/Coefficient/main.c|20|warning: ignoring return value of ‘scanf’ declared with attribute ‘warn_unused_result’ [-Wunused-result]|
||=== Build finished: 0 error(s), 2 warning(s) (0 minute(s), 0 second(s)) ===|

Warnings like that often provide a clue as to some possible undefined or unwanted behavior in a program even if the compilation is successful.

Refactoring your code to eliminate the untested "scanf" calls and utilize the conditioned calls, following is the resulting sample code.

#include <stdio.h>

unsigned long long bin_cof ( int bc_n, int bc_k )
{
    //calculate pochhammer symbol n_k
    int i = 0 ;
    unsigned long long poc = 1 ;
    for ( ; i < bc_k ; i++ )
    {
        poc = poc * ( bc_n - i ) ;
    }

    //calculate factorial k!
    i = 1 ;
    unsigned long long fac = 1 ;
    for ( ; i < bc_k ; i++ )
    {
        fac = fac * ( i + 1 ) ;
    }

    //calculate binomial coefficient
    return poc / fac ;
}

int main (  )
{
    int n, k;                       /* Preference to define data elements at the beginning when possible */

    printf ( "Give me an n : " ) ;

    if ( scanf ( "%d", &n ) != 1 )  /* Removed extraneous scanf calls and used tested scanf calles       */
    {
        printf ( "!!Failed!!" ) ;
        return 1 ;
    }

    printf ( "Give me a k : " ) ;

    if ( scanf ( "%d", &k ) != 1 )
    {
        printf ( "!!Failed!!" ) ;
        return 1 ;
    }

    printf ( "\n%dC%d = %llu\n\n", n, k, bin_cof ( n, k ) ) ;

    return 0 ;
}

FYI, I also removed your call to the "main" function within your code. I am guessing that you were tapping some experience with Python where a "main" function is defined and then called, but that is not necessary here. In fact, that would probably cause a continual recursive call which would be undesired. With that, the compilation is clean.

-------------- Build: Release in Coefficient (compiler: GNU GCC Compiler)---------------

gcc -Wall -O2  -c /home/craig/C_Programs/Console/Coefficient/main.c -o obj/Release/main.o
gcc  -o bin/Release/Coefficient obj/Release/main.o  -s  
Output file is bin/Release/Coefficient with size 14.13 KB
Process terminated with status 0 (0 minute(s), 0 second(s))
0 error(s), 0 warning(s) (0 minute(s), 0 second(s))

In testing this refactored code, following is some sample terminal output.

craig@Vera:~/C_Programs/Console/Coefficient/bin/Release$ ./Coefficient 
Give me an n : 4
Give me a k : 5

4C5 = 0

The takeaway from this is probably getting more familiar with the various methods of requesting data input along with testing. There are plenty of tutorials both printed and online.