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.

Answer 1

If each car choice is determined by a color AND a style, then the total number of possible outcomes equals (number of colors) × (number of styles). We are told there are 8 possible outcomes, so the two numbers must be positive integers whose product is 8.

The factor pairs of 8 are:
- 1 color and 8 styles
- 2 colors and 4 styles
- 4 colors and 2 styles
- 8 colors and 1 style

Any of those pairs would give 8 outcomes. A realistic example is 4 colors and 2 styles (4 × 2 = 8); listing colors A–D and styles S1–S2 produces the 8 possible color/style combinations.