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)