Recursive Program - Choose K Objects Out Of N

I recently wrote a simple recursive program that chooses K objects out of N (I was asked to use the variables N choose the R, however) total objects. Here is the code:

int n = 0;
int r = 0;
//the total number of objects defaults to 0
String nChoice = JOptionPane.showInputDialog(null, "How many objects are there to choose from?");
String rChoice = JOptionPane.showInputDialog(null, "How many object are to be chosen from this group?");
try {
n = Integer.parseInt(nChoice);

[Code] ....

It works fine, however in my class we were given two different formula to implement into our code. I used the one above, obviously. However, the second formula we were given was:

C(n,R) = n!
-------(R!(n-R)!)

I had to get the spacing right.

How do I read this formula? How could it be implemented? What are the benefits (if there are any) from using one method over the other? Which method of calculating N choose K (or, in my case, N choose R) would be more widely accepted?