5.1 fundamental counting principle
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The document discusses using the fundamental counting principle to calculate the number of possible routes when traveling between multiple locations. It provides examples of calculating the number of routes from Southfork to Goodsoil by multiplying the number of road options at each location. It then applies the same principle to calculate the number of possible round trips between Southfork and Goodsoil without repeating roads. The fundamental counting principle states that if the first choice can be made in m ways and the second choice can be made in n ways, then there are m × n ways to select both.
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5.1 fundamental counting principle
- 1. Unit 5: Permutations and Combinations 5.1 Fundamental Counting Principle (p. 373 – 378)
- 2. Consider the following: There are 4 roads from Southfork to Westward, 3 roads from Westward to Consort and 2 roads from Consort to Goodsoil. How many different routes can be taken to travel from Southfork to Goodsoil? Southfork Westward Consort Goodsoil 4 3 2 4 × 3 × 2 = 24 “routes” from Southfork to Goodsoil
- 3. How many routes from Southfork to Goodsoil and back if no road may be taken more than once? 4 × 3 × 2 × 1 × 2 × 3 = 144 144 routes from Southfork to Goodsoil and back without taking a road more than once. Southfork Westward Consort Goodsoil 4 3 2 THERE Southfork Westward Consort 3 2 1 BACK
- 4. FUNDAMENTAL COUNTING PINCIPLE If the first choice can be made in m ways, and the second in n ways, then there are m × n ways to select m and n .
- 12. Homework p. 375 – 378 (#1 – 14)