Adele also must choose between leather or cloth seats for her vehicle. Leather seats come in three color choices; brown, black, and blue. Cloth seats come in two color choices; tan and gray. Using multiplication, Adele says she has (2)(3)(2), or a total of 12, choices for seat covers. Is she correct? Explain why or why not.
Answers
Answer:
Adele is not correct. There are only 5 choices. Here, we are not able to use the fundamental counting principle because there are different choices for each material.
Step-by-step explanation:
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No, Adele is not correct.
Given:
Color choices for leather seats=3
Color choices for cloth seats=2
To find:
The number of choices for seat covers
Solution:
We can find the number by following the given steps-
We know that the number of choices can be calculated by using the concept of combinations.
The total number of combinations= nCr!/n!(n-r)!
Here n refers to the total number of choices available, r stands for the number of choices to be made.
So, the number of choices available for leather seats=3 (brown, black, and blue)
The number of choices available for cloth seats=2 (tan and gray)
Total number of choices= leather+cloth=3+2=5
Choices to be made=1
The number of choices available to Adele= 5!/ 1!×(5-1)!
=5!/4!
=5×4!/4!
=5
Adele has 5 choices for seat covers because she can choose only one type of cover at a time. The cover can be brown leather, black leather, blue leather, tan cloth, or gray cloth.
Therefore, Adele has 5 options of seat covers to choose from.