Question

understanding the size of a sample space
the smith family is shopping for a new car and they are basing their decision on color and style. explain how many color choices and how many style choices they might have if there are 8 possible outcomes. justify your answer.

Explanation:

Step1: Recall counting principle

The total number of outcomes is the product of the number of color - choices and style - choices. Let the number of color choices be $c$ and the number of style choices be $s$. Then the total number of outcomes $N = c\times s$.

Step2: Find factor pairs of 8

We know that $N = 8$. The factor pairs of 8 are: $(1,8)$ since $1\times8 = 8$, $(2,4)$ since $2\times4 = 8$, $(4,2)$ since $4\times2 = 8$ and $(8,1)$ since $8\times1 = 8$.

Answer:

They could have 1 color choice and 8 style choices, 8 color choices and 1 style choice, 2 color choices and 4 style choices, or 4 color choices and 2 style choices. This is because by the fundamental counting principle, the total number of outcomes (8 in this case) is the product of the number of color choices and the number of style choices, and the factor - pairs of 8 give us the possible combinations of color and style choices.