Transcription of 35 Permutations, Combinations and Proba- bility
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35 Permutations, Combinations and Proba- bility
35 Permutations, Combinations and Proba- bilityThus far we have been able to list the elements of a sample space by drawinga tree diagram. For large sample spaces tree diagrams become very complexto construct. In this section we discuss counting techniques for finding thenumber of elements of a sample space or an event without having to list the following problem: In how many ways can 8 horses finish in arace (assuming there are no ties)? We can look at this problem as a decisionconsisting of 8 steps. The first step is the possibility of a horse to finishfirst in the race, the second step the horse finishes second, .. , the 8th stepthe horse finishes 8th in the race. Thus, by the Fundamental Principle ofcounting there are8 7 6 5 4 3 2 1 = 40,320 waysThis problem exhibits an example of an ordered arrangement, that is, theorder the objects are arranged is important.
want to know the number of ways in which r objects can be selected from n distinct objects in arbitrary order. For example, when selecting a two-person committee from a club of 10 members the order in the committee is irrelevant. That is choosing Mr A and Ms B in a committee is the same as 4
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