C Homework Assignment:
Compute choose function

Design and write a complete C program including adequate comments to compute C(n, r).  This function is known as the choose function, and is defined as the number of r element subsets of an n element set.  So C(5, 2) = 10 because there are ten possible two element subsets from a set of 5 elements.  Similarly, C(4, 1) = 4, C(4, 4) = 1, and C(4, 0) = 1.

Mathematically the choose function is defined as:

C(n, r) = n! / (R! * (n - r)! )

Where n and r are positive integers (or zero), and "!" means factorial, so C(5, 2) = 5! / (2! * 3!) = 120 / (2 * 6) = 120 / 12 = 10.  Note that 0! (zero factorial) is defined to be 1 (one).

You must use exactly and only the following four functions in your program whose prototypes are as shown, and each performs the following tasks only:

The program should compile perfectly (without errors) and execute without error.


The number of possible 5-card poker hands is C( 52, 5 ), which equals 2598960.  Yet even thought this value will fit into a long (or a 4 byte int), it is likely that trying to compute C( 52, 5 ) will cause an error or a system crash.  (If you don't get a problem on that, try C( 52, 13 ) which is the number of possible bridge hands.)  Why?  Indicate how you would fix the problem.  (It's not necessary to provide a second program, just briefly write in English what you would do.)

Send comments and mail to pollock@acm.org.