CISC 102 Lecture Notes - Lecture 28: Complex Instruction Set Computing

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Suppose we want to count the num of different 5-card poker hands. Thus, we are interested in the num of ways of selecting 5 from 52 without regard to the way that they are ordered. 52!/47: how do we put these two answers together to count the num of ways to make an unordered selection of 5 of the. Divide the answer to (2) by the answer to (1), yielding: We can use the balls in a bag analogy to count combinations. In this case, we count the num of different ways of selecting distinct balls without ordering. The counting technique is a 2 step process: count the num of ways to select k balls from a bag of n balls without ordering, divide by the num of ways to order the k selected balls. The outcome of this process yields the formula: We have seen this expression before and the shorthand is as follows:

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