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The sample-point method for calculating probabilities and tools for counting sample points in the context of stat 3401, introductory probability theory. Topics covered include calculating probabilities using the sample-point method, counting sample points using the mn rule and permutations, and understanding the difference between permutations and combinations. Examples include calculating probabilities of selecting applicants, tossing dice, and the birthday problem.
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o The “mn rule” can be extended to any number of sets. Given three sets of elements a 1 , a 2 , …,a m , b 1 , b 2 , …,b n and c 1 , c 2 , …,c p, the number of distinct triplets (a i ,b j ,c k) containing one element from each set is equal to mnp. (Why?)
o The terms are called “binomial coefficients” because they occur in the “binomial
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