This question is my own invention. You can add any restriction when you feel confused.
Assume there are $8$ distinguishable balls outside boxes and $5$ boxes, randomly draw $5$ balls to $5$ boxes respectively, $1$ ball $1$ box, but there is a condition that
- divide $5$ boxes into $3$ groups,
- group $1$ is box $1$, box $2$, box $3$; group $2$ is box $2$, box $3$, box $4$; group $3$ is box $3$, box $4$, box $5$
After ball drawn, will return back, every draw is from $8$ balls, just mark the ball number on the box to do a record
The important criterion is that $3$ groups must be distinct that for example group $1$ and group $2$ can not be $2,3,5$ at the same, but it can be $2,3,5$ and $3,5,2$ respectively
If there are more boxes, any two of groups can not be can not be $2,3,5$ at the same time in example.
If it can be generalized to the case of $n$ balls and $r$ boxes, it would be more powerful.
How many ways do balls put into the boxes that satisfy above criteria?
better use $(z+z^2+z^3+z^4+z^5+z^6+z^7+z^8)^5$ i guess divided by or minus $(z+z^2+z^3)^3$ ($z+z^2+z^3)$, $(z^2+z^3+z^4)$... i am confusing about the overlapping
從波波池中任意抽八個不同波放入五個相同的箱, 每個箱放一個波, 記錄波的編號在箱上面, 再把波放回波波池, 跟著再抽第二次放落第二個箱 如此類推.
但有一個條件,
五個箱分三組, 第一第二第三合成一組, 第二第三第四合成一組, 第三第四第五合成一組 抽波時要留意這三組都要不同, 例如 2,3,5 和 3,5,6 就是不同
用另一個角度說, 抽完所有波後, 任意兩個連續的箱的右邊的一個箱(也就是第三個箱) 和 另外任意兩個連續的箱的右邊的一個箱(也就是第三個箱) 一定要相同如果 任意兩個連續的箱 和 另外任意兩個連續的箱 是一樣 <-- 這個才是最重要的特色
