Project Euler：Problem 53 Combinatoric selections

There are exactly ten ways of selecting three from five, 12345:

123, 124, 125, 134, 135, 145, 234, 235, 245, and 345
In combinatorics, we use the notation, 5C3 = 10.
In general,

nCr =

n! r!(n−r)!

,where r ≤ n, n! = n×(n−1)×...×3×2×1, and 0! = 1.

It is not until n = 23, that a value exceeds one-million: 23C10 = 1144066.
How many, not necessarily distinct, values of nCr,
for 1 ≤ n ≤ 100, are greater than one-million?

#include <iostream>
#include <string>
using namespace std;

int c[101][101];

int main()
{
	memset(c, 0, sizeof(c));
	
	for (int i = 1; i <= 100; i++)
	{
		c[0][i] = 1;
		c[1][i] = i;
		c[i][i] = 1;
		c[i - 1][i] = i;
	}
	int count = 0;
	for (int n = 2; n <= 100; n++)
	{
		for (int r = 2; r < n; r++)
		{
			c[r]
 = c[r][n - 1] + c[r - 1][n - 1];
			if (c[r]
>1000000)
			{
				c[r]
 = 1000001;
				count++;
			}
		}
	}
	cout << count << endl;
	system("pause");
	return 0;
}