Numerically Computing Binomial Coefficient

So I was given the program that calculates N!/[R!(N-R)!] and it has an overflow error after it passes N=18 and then starts spiting out incorrect answer. I'm supposed to figure out a way to protect the user from getting erroneous results when computing the formula (i.e. N!/[R!(N-R)!]).

HERE IS THE PROGRAM:

public class Combination {
private static final int defaultNMax = 30;
public Combination() {}
int compute(int N, int R) {
int i;
int numerator;
int denominator;
numerator = 1;

[Code] .....

HERE ARE THE RESULTS IF YOU WANT TO SEE THEM:

N=1C(1,0)=1
N=2C(2,1)=2
N=3C(3,1)=3
N=4C(4,2)=6
N=5C(5,2)=10
N=6C(6,3)=20
N=7C(7,3)=35

[Code] .....