The World is a Theatre（组合数学）

There are n boys and m girls attending a theatre club. To set a play “The Big Bang Theory”, they need to choose a group containing exactly t actors containing no less than 4 boys and no less than one girl. How many ways are there to choose a group? Of course, the variants that only differ in the composition of the troupe are considered different.

Perform all calculations in the 64-bit type: long long for С/С++, int64 for Delphi and long for Java.

Input
The only line of the input data contains three integers n, m, t (4 ≤ n ≤ 30, 1 ≤ m ≤ 30, 5 ≤ t ≤ n + m).

Output
Find the required number of ways.

Please do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specificator.

Examples
Input
5 2 5
Output
10
Input
4 3 5
Output
3
挺水的这道题，但是一次做对也不是很容易。首先打表求出组合数。其次数组不要开得太小，dp[i][j]，如果j>i的时候，就是0。
代码如下：

#include
#define ll long long
using namespace std;

const int maxx=100;
int n,m,t;
ll dp[maxx][maxx];

inline void init()
{
	memset(dp,0,sizeof(dp));
	for(int i=0;i<=30;i++)
	{
		dp[0][i]=0;
		dp[i][0]=1ll;
	}
	for(int i=1;i<=30;i++)
	{
		for(int j=1;j<=i;j++)
		{
			dp[i][j]=(dp[i-1][j]+dp[i-1][j-1]);
		}
	}
}
int main()
{
	init();
	while(~scanf("%d%d%d",&n,&m,&t))
	{
		if(t<5||n<4||m<1) puts("0");
		else
		{
			ll sum=0;
			for(int i=4;i<=n&&t-i>=1;i++)
			{
				sum+=dp[n][i]*dp[m][t-i];//单纯的排列组合
			}
			printf("%I64d\n",sum);
		}
	}
}

努力加油a啊，(^o)/~