从五个球中选出3个枚举的简单运用

有红，黄，蓝，白，黑，5中颜色求若干个，每次取3个不同颜色的球，问有多少种取法：

#include<iostream>
using namespace std;
int main(){
    enum color{red,yellow,blue,white,black};
    enum color pri;
    int n,loop,i,j,k;
    char c;
    n=0;
    for(i=red;i<=black;i++){
        for(j=red;j<=black;j++){
            if(i!=j){
                for(k=red;k<=black;k++)
                    if(k!=i&&k!=j){
                        n++;
                        cout.width(4);
                        cout<<n;
                        for(loop=1;loop<=3;loop++){
                            switch(loop){
                                case 1:pri=(enum color)i;break;
                                case 2:pri=(enum color)j;break;
                                case 3:pri=(enum color)k;break;
                                default:break;
                            }
                            switch(pri){
                                case red:cout<<"  red";break;
                                case yellow:cout<<"  yellow";break;
                                case blue:cout<<"  blue";break;
                                case white:cout<<"  white";break;
                                case black:cout<<"  black";break;
                            }
                        }cout<<endl;
                        
                    }
            }
        }

    }
    cout<<"total:"<<n<<endl;
    system("pause");
    return 0;
}