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Counting Principle and Tree Diagram

A specific brand of bike comes in two frames, for males or females. Each frame comes in a choice of two colors, red and blue, and with a choice of three seats, soft, medium, and hard.

a) Use the counting principle to determine the number of different arrangements of bicycles that are possible.

b) Construct a tree diagram illustrating all the different arrangements of bicycles that are possible.

c) List the sample space.

Solution Preview

According to the problem, there are 2 frames, 2 colors, and 3 seats available to make a bicycle.

A) The counting principle says that the total possible number of ways all events can performed is the product of the possible number of ways each individual event can be performed. That means that the total arrangements of bicycles that can be made can be calculated as the ...

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