用java编程或者是用排列组合做一个题啊

Question

有八种颜色的球（不限个数），从中选出四个组成一组,最多能有多少种不同的组 都是一样的球  就颜色可能不一样
题目的意思相当于 给4个相同的球都涂颜色,有8种颜色,最多有多少种涂法?

Answer 1

很典型的数据结构里的结果就是C8取4除以4的阶乘即：8*7*6*5/4!扩展一下，如果是m种总颜色中取n种颜色那么结果就是
m*(m-1)*(m-2)*.../n!
分母就是m往下乘，乘数个数是n个

Answer 2

补充一下，n后面的感叹号不是标点符号，而是阶乘
n!=n*(n-1)*...*1
比如
4! = 4*3*2*1

Answer 3

假设abcd代表4种颜色
以下情况是有可能出现的
abcd,aaaa,aaab
abcd和acdb是一样的,属于一种情况.
我觉得你的这种算法有问题.首先8*7*6*5的意思就否定了有颜色相同的可能.

Answer 4

我的java代码:public static void main(String[] args) {
// TODO Auto-generated method stub
int sum =0;
for(int a = 0;a < 5;a++){
for(int b = 0;b < 5;b++){
for(int c = 0;c < 5;c++){
for(int d = 0;d < 5;d++){
for(int e = 0;e < 5;e++){
for(int f = 0;f < 5;f++){
for(int g = 0;g < 5;g++){
for(int h = 0;h < 5;h++){
if(a+b+c+d+e+f+g+h == 4){
System.out.println(a+"a"+b+"b"+c+"c"+d+"d"+e+"e"+f+"f"+g+"g"+h+"h");
sum++;
}
}
}
}
}
}
}
}
}
System.out.println(sum);
}
我的打印结果:
0a0b0c0d0e0f0g4h
0a0b0c0d0e0f1g3h
0a0b0c0d0e0f2g2h
0a0b0c0d0e0f3g1h
0a0b0c0d0e0f4g0h
0a0b0c0d0e1f0g3h
0a0b0c0d0e1f1g2h
0a0b0c0d0e1f2g1h
0a0b0c0d0e1f3g0h
0a0b0c0d0e2f0g2h
0a0b0c0d0e2f1g1h
0a0b0c0d0e2f2g0h
0a0b0c0d0e3f0g1h
0a0b0c0d0e3f1g0h
0a0b0c0d0e4f0g0h
0a0b0c0d1e0f0g3h
0a0b0c0d1e0f1g2h
0a0b0c0d1e0f2g1h
0a0b0c0d1e0f3g0h
0a0b0c0d1e1f0g2h
0a0b0c0d1e1f1g1h
0a0b0c0d1e1f2g0h
0a0b0c0d1e2f0g1h
0a0b0c0d1e2f1g0h
0a0b0c0d1e3f0g0h
0a0b0c0d2e0f0g2h
0a0b0c0d2e0f1g1h
0a0b0c0d2e0f2g0h
0a0b0c0d2e1f0g1h
0a0b0c0d2e1f1g0h
0a0b0c0d2e2f0g0h
0a0b0c0d3e0f0g1h
0a0b0c0d3e0f1g0h
0a0b0c0d3e1f0g0h
0a0b0c0d4e0f0g0h
0a0b0c1d0e0f0g3h
0a0b0c1d0e0f1g2h
0a0b0c1d0e0f2g1h
0a0b0c1d0e0f3g0h
0a0b0c1d0e1f0g2h
0a0b0c1d0e1f1g1h
0a0b0c1d0e1f2g0h
0a0b0c1d0e2f0g1h
0a0b0c1d0e2f1g0h
0a0b0c1d0e3f0g0h
0a0b0c1d1e0f0g2h
0a0b0c1d1e0f1g1h
0a0b0c1d1e0f2g0h
0a0b0c1d1e1f0g1h
0a0b0c1d1e1f1g0h
0a0b0c1d1e2f0g0h
0a0b0c1d2e0f0g1h
0a0b0c1d2e0f1g0h
0a0b0c1d2e1f0g0h
0a0b0c1d3e0f0g0h
0a0b0c2d0e0f0g2h
0a0b0c2d0e0f1g1h
0a0b0c2d0e0f2g0h
0a0b0c2d0e1f0g1h
0a0b0c2d0e1f1g0h
0a0b0c2d0e2f0g0h
0a0b0c2d1e0f0g1h
0a0b0c2d1e0f1g0h
0a0b0c2d1e1f0g0h
0a0b0c2d2e0f0g0h
0a0b0c3d0e0f0g1h
0a0b0c3d0e0f1g0h
0a0b0c3d0e1f0g0h
0a0b0c3d1e0f0g0h
0a0b0c4d0e0f0g0h
0a0b1c0d0e0f0g3h
0a0b1c0d0e0f1g2h
0a0b1c0d0e0f2g1h
0a0b1c0d0e0f3g0h
0a0b1c0d0e1f0g2h
0a0b1c0d0e1f1g1h
0a0b1c0d0e1f2g0h
0a0b1c0d0e2f0g1h
0a0b1c0d0e2f1g0h
0a0b1c0d0e3f0g0h
0a0b1c0d1e0f0g2h
0a0b1c0d1e0f1g1h
0a0b1c0d1e0f2g0h
0a0b1c0d1e1f0g1h
0a0b1c0d1e1f1g0h
0a0b1c0d1e2f0g0h
0a0b1c0d2e0f0g1h
0a0b1c0d2e0f1g0h
0a0b1c0d2e1f0g0h
0a0b1c0d3e0f0g0h
0a0b1c1d0e0f0g2h
0a0b1c1d0e0f1g1h
0a0b1c1d0e0f2g0h
0a0b1c1d0e1f0g1h
0a0b1c1d0e1f1g0h
0a0b1c1d0e2f0g0h
0a0b1c1d1e0f0g1h
0a0b1c1d1e0f1g0h
0a0b1c1d1e1f0g0h
0a0b1c1d2e0f0g0h
0a0b1c2d0e0f0g1h
0a0b1c2d0e0f1g0h
0a0b1c2d0e1f0g0h
0a0b1c2d1e0f0g0h
0a0b1c3d0e0f0g0h
0a0b2c0d0e0f0g2h
0a0b2c0d0e0f1g1h
0a0b2c0d0e0f2g0h
0a0b2c0d0e1f0g1h
0a0b2c0d0e1f1g0h
0a0b2c0d0e2f0g0h
0a0b2c0d1e0f0g1h
0a0b2c0d1e0f1g0h
0a0b2c0d1e1f0g0h
0a0b2c0d2e0f0g0h
0a0b2c1d0e0f0g1h
0a0b2c1d0e0f1g0h
0a0b2c1d0e1f0g0h
0a0b2c1d1e0f0g0h
0a0b2c2d0e0f0g0h
0a0b3c0d0e0f0g1h
0a0b3c0d0e0f1g0h
0a0b3c0d0e1f0g0h
0a0b3c0d1e0f0g0h
0a0b3c1d0e0f0g0h
0a0b4c0d0e0f0g0h
0a1b0c0d0e0f0g3h
0a1b0c0d0e0f1g2h
0a1b0c0d0e0f2g1h
0a1b0c0d0e0f3g0h
0a1b0c0d0e1f0g2h
0a1b0c0d0e1f1g1h
0a1b0c0d0e1f2g0h
0a1b0c0d0e2f0g1h
0a1b0c0d0e2f1g0h
0a1b0c0d0e3f0g0h
0a1b0c0d1e0f0g2h
0a1b0c0d1e0f1g1h
0a1b0c0d1e0f2g0h
0a1b0c0d1e1f0g1h
0a1b0c0d1e1f1g0h
0a1b0c0d1e2f0g0h
0a1b0c0d2e0f0g1h
0a1b0c0d2e0f1g0h
0a1b0c0d2e1f0g0h
0a1b0c0d3e0f0g0h
0a1b0c1d0e0f0g2h
0a1b0c1d0e0f1g1h
0a1b0c1d0e0f2g0h
0a1b0c1d0e1f0g1h
0a1b0c1d0e1f1g0h
0a1b0c1d0e2f0g0h
0a1b0c1d1e0f0g1h
0a1b0c1d1e0f1g0h
0a1b0c1d1e1f0g0h
0a1b0c1d2e0f0g0h
0a1b0c2d0e0f0g1h
0a1b0c2d0e0f1g0h
0a1b0c2d0e1f0g0h
0a1b0c2d1e0f0g0h
0a1b0c3d0e0f0g0h
0a1b1c0d0e0f0g2h
0a1b1c0d0e0f1g1h
0a1b1c0d0e0f2g0h
0a1b1c0d0e1f0g1h
0a1b1c0d0e1f1g0h
0a1b1c0d0e2f0g0h
0a1b1c0d1e0f0g1h
0a1b1c0d1e0f1g0h
0a1b1c0d1e1f0g0h
0a1b1c0d2e0f0g0h
0a1b1c1d0e0f0g1h
0a1b1c1d0e0f1g0h
0a1b1c1d0e1f0g0h
0a1b1c1d1e0f0g0h
0a1b1c2d0e0f0g0h
0a1b2c0d0e0f0g1h
0a1b2c0d0e0f1g0h
0a1b2c0d0e1f0g0h
0a1b2c0d1e0f0g0h
0a1b2c1d0e0f0g0h
0a1b3c0d0e0f0g0h
0a2b0c0d0e0f0g2h
0a2b0c0d0e0f1g1h
0a2b0c0d0e0f2g0h
0a2b0c0d0e1f0g1h
0a2b0c0d0e1f1g0h
0a2b0c0d0e2f0g0h
0a2b0c0d1e0f0g1h
0a2b0c0d1e0f1g0h
0a2b0c0d1e1f0g0h
0a2b0c0d2e0f0g0h
0a2b0c1d0e0f0g1h
0a2b0c1d0e0f1g0h
0a2b0c1d0e1f0g0h
0a2b0c1d1e0f0g0h
0a2b0c2d0e0f0g0h
0a2b1c0d0e0f0g1h
0a2b1c0d0e0f1g0h
0a2b1c0d0e1f0g0h
0a2b1c0d1e0f0g0h
0a2b1c1d0e0f0g0h
0a2b2c0d0e0f0g0h
0a3b0c0d0e0f0g1h
0a3b0c0d0e0f1g0h
0a3b0c0d0e1f0g0h
0a3b0c0d1e0f0g0h
0a3b0c1d0e0f0g0h
0a3b1c0d0e0f0g0h
0a4b0c0d0e0f0g0h
1a0b0c0d0e0f0g3h
1a0b0c0d0e0f1g2h
1a0b0c0d0e0f2g1h
1a0b0c0d0e0f3g0h
1a0b0c0d0e1f0g2h
1a0b0c0d0e1f1g1h
1a0b0c0d0e1f2g0h
1a0b0c0d0e2f0g1h
1a0b0c0d0e2f1g0h
1a0b0c0d0e3f0g0h
1a0b0c0d1e0f0g2h
1a0b0c0d1e0f1g1h
1a0b0c0d1e0f2g0h
1a0b0c0d1e1f0g1h
1a0b0c0d1e1f1g0h
1a0b0c0d1e2f0g0h
1a0b0c0d2e0f0g1h
1a0b0c0d2e0f1g0h
1a0b0c0d2e1f0g0h
1a0b0c0d3e0f0g0h
1a0b0c1d0e0f0g2h
1a0b0c1d0e0f1g1h
1a0b0c1d0e0f2g0h
1a0b0c1d0e1f0g1h
1a0b0c1d0e1f1g0h
1a0b0c1d0e2f0g0h
1a0b0c1d1e0f0g1h
1a0b0c1d1e0f1g0h
1a0b0c1d1e1f0g0h
1a0b0c1d2e0f0g0h
1a0b0c2d0e0f0g1h
1a0b0c2d0e0f1g0h
1a0b0c2d0e1f0g0h
1a0b0c2d1e0f0g0h
1a0b0c3d0e0f0g0h
1a0b1c0d0e0f0g2h
1a0b1c0d0e0f1g1h
1a0b1c0d0e0f2g0h
1a0b1c0d0e1f0g1h
1a0b1c0d0e1f1g0h
1a0b1c0d0e2f0g0h
1a0b1c0d1e0f0g1h
1a0b1c0d1e0f1g0h
1a0b1c0d1e1f0g0h
1a0b1c0d2e0f0g0h
1a0b1c1d0e0f0g1h
1a0b1c1d0e0f1g0h
1a0b1c1d0e1f0g0h
1a0b1c1d1e0f0g0h
1a0b1c2d0e0f0g0h
1a0b2c0d0e0f0g1h
1a0b2c0d0e0f1g0h
1a0b2c0d0e1f0g0h
1a0b2c0d1e0f0g0h
1a0b2c1d0e0f0g0h
1a0b3c0d0e0f0g0h
1a1b0c0d0e0f0g2h
1a1b0c0d0e0f1g1h
1a1b0c0d0e0f2g0h
1a1b0c0d0e1f0g1h
1a1b0c0d0e1f1g0h
1a1b0c0d0e2f0g0h
1a1b0c0d1e0f0g1h
1a1b0c0d1e0f1g0h
1a1b0c0d1e1f0g0h
1a1b0c0d2e0f0g0h
1a1b0c1d0e0f0g1h
1a1b0c1d0e0f1g0h
1a1b0c1d0e1f0g0h
1a1b0c1d1e0f0g0h
1a1b0c2d0e0f0g0h
1a1b1c0d0e0f0g1h
1a1b1c0d0e0f1g0h
1a1b1c0d0e1f0g0h
1a1b1c0d1e0f0g0h
1a1b1c1d0e0f0g0h
1a1b2c0d0e0f0g0h
1a2b0c0d0e0f0g1h
1a2b0c0d0e0f1g0h
1a2b0c0d0e1f0g0h
1a2b0c0d1e0f0g0h
1a2b0c1d0e0f0g0h
1a2b1c0d0e0f0g0h
1a3b0c0d0e0f0g0h
2a0b0c0d0e0f0g2h
2a0b0c0d0e0f1g1h
2a0b0c0d0e0f2g0h
2a0b0c0d0e1f0g1h
2a0b0c0d0e1f1g0h
2a0b0c0d0e2f0g0h
2a0b0c0d1e0f0g1h
2a0b0c0d1e0f1g0h
2a0b0c0d1e1f0g0h
2a0b0c0d2e0f0g0h
2a0b0c1d0e0f0g1h
2a0b0c1d0e0f1g0h
2a0b0c1d0e1f0g0h
2a0b0c1d1e0f0g0h
2a0b0c2d0e0f0g0h
2a0b1c0d0e0f0g1h
2a0b1c0d0e0f1g0h
2a0b1c0d0e1f0g0h
2a0b1c0d1e0f0g0h
2a0b1c1d0e0f0g0h
2a0b2c0d0e0f0g0h
2a1b0c0d0e0f0g1h
2a1b0c0d0e0f1g0h
2a1b0c0d0e1f0g0h
2a1b0c0d1e0f0g0h
2a1b0c1d0e0f0g0h
2a1b1c0d0e0f0g0h
2a2b0c0d0e0f0g0h
3a0b0c0d0e0f0g1h
3a0b0c0d0e0f1g0h
3a0b0c0d0e1f0g0h
3a0b0c0d1e0f0g0h
3a0b0c1d0e0f0g0h
3a0b1c0d0e0f0g0h
3a1b0c0d0e0f0g0h
4a0b0c0d0e0f0g0h
330其中abcdefgh分别代表8种不同的颜色,前面的数字代表这种颜色出现的次数.比如:2a1b0c0d0e0f1g0h
表示a颜色出现了2次,b颜色出现了1次,g颜色出现了1次,其它的颜色都没有出现.也就是说4个球中有两个a颜色的球,1个b颜色的球,1个g颜色的球.
最后打印出来的总条数是330条,也就是有330种情况.
为什么没人的结果和我一样?这种算法有道理吗?