When the Smith family decided to have their new house build, they found that there were 60 different choices involving location, style, and color. If they had their choice of 2 locations and 5 styles, how many choices of color did they have? This is 6 right?
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Oh, the Smith family sure had a lot on their plate with all those choices! But let me tell you, it's not just 6 colors they had to choose from.
See, if they had 2 locations and 5 styles, you can think of it like this: they could have picked location 1 and style 1, location 1 and style 2, location 1 and style 3, location 1 and style 4, or location 1 and style 5. So that's already 5 possibilities with just location 1!
Then, they could have picked location 2 and style 1, location 2 and style 2, location 2 and style 3, location 2 and style 4, or location 2 and style 5. That's another 5 possibilities with location 2!
And since they had 2 locations, they had a total of 10 possibilities with just the styles and locations. But wait, there were 60 different choices in total, so if we subtract those 10 choices, we're left with 50 choices of color! Quite a colorful decision-making process, wouldn't you say?
To determine the number of choices of color the Smith family had, we need to multiply the number of choices for each category: location, style, and color.
The Smith family had two choices for the location:
- Choice 1: Location A
- Choice 2: Location B
They also had five choices for the style:
- Choice 1: Style 1
- Choice 2: Style 2
- Choice 3: Style 3
- Choice 4: Style 4
- Choice 5: Style 5
Now, since there were a total of 60 choices, we can find the number of choices of color by dividing the total number of choices by the multiplication of the number of choices for the location and the number of choices for the style:
Total Choices = Number of choices for Location × Number of choices for Style × Number of choices for Color
60 = 2 (choices for location) × 5 (choices for style) × Number of choices for color
To find the number of choices for color, we rearrange the formula and solve for Number of choices for color:
Number of choices for color = Total Choices / (Number of choices for location × Number of choices for style)
Number of choices for color = 60 / (2 × 5)
Number of choices for color = 60 / 10
Number of choices for color = 6
Therefore, the Smith family had 6 choices of color for their new house, not 6.