9-3 The Fundamental Counting Principle Pages-378-380 Indicator(s)  D7.

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9-3 The Fundamental Counting Principle Pages Indicator(s)  D7

In the previous section, you learned to use tree diagrams to find the number of possible outcomes in a sample space. This section uses the fundamental counting principle This section uses the fundamental counting principle to find the same information. The fundamental counting principle uses multiplication to find the number of possible outcomes. The fundamental counting principle states that: If event M can occur m ways and is followed by N that can occur n ways, then the event M followed by N can occur m × n ways.

Example: The table below shows the shirts, shorts, and shoes in Gerry’s wardrobe. How many possible outfits can he choose consisting of one shirt, one pair of shorts, and one pair of shoes? shirtsshortsshoesredbluewhiteyellowbeigegreenbluebrownblack 4 shirts × 3 shorts × 2 shoes 4 × 3 × 2 = 24 Gerry has 24 possible outfits.

You try… An orchestra has one opening for a violinist, one opening for a cellist, and one opening for an oboist. Three musicians are trying out for violin, five for cello, and three for oboe. Find the number of ways the openings can be filled.