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7.4Permutations and Combinations - Washington State …

Permutations and CombinationsThe multiplication principle discussed in the preceding section can beused to develop two additional counting devices that are extremelyuseful in more complicated counting problems. Both of these using the multiplication principle, we encountered expressionssuch as26 25 24or8 7 6where each natural number factor is decreased by 1 as we move fromleft to right. The factors in the following product continue to decreaseby 1 until a factor of 1 is reached:5 4 3 2 1 Products like this are encountered so frequently in counting problemsthat it is useful to express them in a concise notation. The product ofthe first n natural numbers is callednfactorialand is denoted byn!. Also, we definezero factorial, 0!

(a)In how many ways can we choose a chairperson, a vice-chairperson, a secretary, and a treasurer, assuming that one person cannot hold more than one position? (b)In how many ways can we choose a subcommittee of 4 people? 9

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