How many ways can you pick k items out of a set of n items?

n!
----------
k!*(n-k)!

The Program

/*
* File: combine.c
* ---------------
* This program tests a function to compute the
* mathematical combination function
* Combinations(n, k), which gives the number
* of ways to choose a subset of k objects from
* a set of n distinct objects.
*/
#include
/* Function prototypes */
int Combinations (int n, int k);
int Factorial (int n);
/* Main program */
main ()
{
int n, k;
printf("Enter number of objects in the set (n)? ");
scanf ("%d", &n);
printf("Enter number to be chosen (k)? ");
scanf ("%d", &k);
printf("C(%d, %d) = %d\n", n, k,
Combinations(n, k));
}
/*
* Function: Combinations
* Usage: ways = Combinations(n, k);
* ---------------------------------
* Implements the Combinations function, which
* returns the number of distinct ways of choosing
* k objects from a set of n objects. In
* mathematics, this function is often written as
* C(n,k), but a function called C is not very
* self-descriptive, particularly in a language
* which has precisely the same name. Implements
* the formula n!/(k! * (n - k)!)
*/
int Combinations(int n, int k)
{
int numerator, denominator, ways;
numerator = Factorial (n);
denominator = Factorial (k) * Factorial (n - k);
ways = numerator / denominator;
return (ways);
}
/*
* Function: Factorial
* Usage: f = Factorial(n);
* ------------------------
* Returns the factorial of the argument n, where
* factorial is defined as the product of all
* integers from 1 up to n.
*/
int Factorial (int n)
{
int product, i;
product = 1;
for (i = 1; i <= n; i++)
{
product *= i;
}
return (product);
}

The Sample Run

lassie% a.out
Enter number of objects in the set (n)? 6
Enter number to be chosen (k)? 2
C(6, 2) = 15
lassie%
lassie% a.out
Enter number of objects in the set (n)? 3
Enter number to be chosen (k)? 2
C(3, 2) = 3
lassie%
lassie% a.out
Enter number of objects in the set (n)? 12
Enter number to be chosen (k)? 4
C(12, 4) = 495
lassie% exit
lassie%