排列组合
可区分的叫做排列 abc P33
不可区分的叫做组合 aaa C33
用下列步骤来作一切的排列组合题:
先考虑是否要分情况考虑
先计算有限制或数目多的字母,再计算无限制,数目少的字母
在计算中永远先考虑组合:先分配,再如何排
例子:
8封相同的信,扔进4个不同的邮筒,要求每个邮筒至少有一封信,问有多少种扔法?
第一步:需要分类考虑既然信是一样的,邮筒不一样,则只考虑4个不同邮筒会出现信的可能性。
第二步:计算数目多或者限制多的字母,由于信一样就不考虑信而考虑邮筒,从下面的几个情况几列式看出每次都从限制多的条件开始作。先选择,再考虑排列。
5个情况如下:
a. 5 1 1 1:4个邮筒中取一个邮筒放5封信其余的3个各放一个的分法:C=4
b.4 2 1 1:同上,一个邮筒4封信,其余三个中间一个有两封,两个有一封:C C=12
c. 3 3 1 1: C =6
d. 3 2 2 1: C C = 12
e. 2 2 2 2 :1
4+12+6+12+1=35种放法
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