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
#SPJ2
