Probability and Statistics -- Introduction to Probability (part II)

1.7 Counting Methods

1.8 Combinatorial Methods

 

所以，在N个元素中选择K个元素子集的组合与两种类型元素在N个位置上K种安排的组合是等价的。

Ordered versus Unordered Samples

样本空间S不考虑序列顺序，概率事件E也不考虑序列顺序，S与E应保持一致。

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1.9 Multinomial Coefficients

把N个不重复的元素，分到K个组中（K>=2），设置j=1,2....k, 则n1+n2+....+nk = N, 

则样本空间S的大小为: N!/n1!n2!n3!......nk!

总结：

1.10 The Probability of a Union of Events

The Union of a Finite Number of Events

A result similar to Theorem 1.10.1 holds for any arbitrary finite number of events, as shown by the following theorem.

For every n events A1, . . . , An,