generalized bernouli trials

generalized bernouli trials - Generalized Bernouli Trials...

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Generalized Bernouli Trials Consider the collection of all possible sequences of A’s, B’s and C’s, in which there are 3 A’s, 2 B’s, and 5C’s. Two examples of such sequences are shown below. ACABCCBACC CBABAACCCC We want to answer the question, “how many different such sequences are there?” To answer this question we first consider a different, but related question. Suppose that we number the A’s from 1 to 3, the B’s
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from 1 to 2 and the C’s from 1 to 5, and consider the collection of numbered sequences of the letters. Examples of such numbered sequences are: A 2 C 1 A 1 B 2 C 4 C 5 B 1 A 3 C 2 C 3 C 2 B 2 A 1 B 1 A 3 A 2 C 4 C 3 C 5 C 1 How many different numbered sequences of 3 A’s, 2 B’s, and 5C’s are there? Since the numbering operation results in 10 completely distinct (distinguishable) objects, there are just 10! (10 factorial) different permutations of their ordering, so there are 10! Different numbered sequences.
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