Answered

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QUESTION 11
A person purchasing a new car has several options: 6 interior color choices, 3 exterior color choices, 2 choices of radios, and 6 choices of
body styles. How many different cars are possible if one choice is made for each option?
60
17
216
208

Sagot :

musiclover10045

Total choices = quantity of each option x each other:

Total choices = 6 x 3 x 2 x 6 = 216

Answer: 216

abbusaicharan02

Total number of different cars possible when one choice is made for each option is 216.

Combination

The way of selecting a fixed entity out of the given options is known as Combination in mathematics.

The formula used for selecting is [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex] where n is the total number of options available and r is the fixed entity.

How to different possible combinations?

Ways of selecting 1 interior color is-

[tex]^6C_1=\dfrac{6!}{1!(6-1)!}\\=6[/tex]

Ways of selecting 1 exterior color is-

[tex]^3C_1=\dfrac{3!}{1!(3-1)!}\\=3[/tex]

Ways of selecting 1 radio color is-

[tex]^2C_1=\dfrac{2!}{1!(2-1)!}\\=2[/tex]

Ways of selecting 1 body style is-

[tex]^6C_1=\dfrac{6!}{1!(6-1)!}\\=6[/tex]

Hence, total number of different cars possible when one choice is made for each option is [tex]6\times 3\times 2\times 6=216[/tex].

Learn more about combinations here- https://brainly.com/question/12629775

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