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如何区别是排列还是组合

EQ3. You will pick two marbles from a bag of 10, without putting the first one back. At least how many of the ten marbles need to be red for you to have a greater than 50% chance of picking two red marbles?
在这个题里,我认为是组合C,而不是排列P。
假设一共{A1,A2,…A10}十个叶子,选出A1A2,或是A2A1不都是一个意思吗。
我不明白为什么是排列
Thanks

其实无论你用排列还是组合都是可以的,看你如何定义样本点(sample point)
这题,如果你定义样本点为组合(combination),
那么:
Random Experiment: pick 2 marbles out of 10
A: pick two marbles
Say we have n red marbles

P(A)=|A|/|Omega|
|Omega|=C(10,2)=10*9/2=45
|A|=C(n,2)=n(n-1)/2

P(A)=n(n-1)/90

如果你把样本点定义为排列:
|Omega|=P(10,2)=10*9=90
|A|=P(n,2)=n(n-1)

P(A)=n(n-1)/90