5.1 fundamental counting principle
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Unit 5: Permutations and Combinations
5.1 Fundamental Counting Principle (p. 373 – 378)
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
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
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.
Homeworkp. 375 – 378 (#1 – 14)