We have that there are [tex]^{27}C_8=2220075[/tex] different groups of 8 cars are possible when selecting the cars.
From the question we are told that:
Number of cars in a line [tex]N_l=8[/tex]
Number of available cars [tex]N_a=27[/tex]
Generally The formulae for combination is
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Generally for our calculations we use combination cause the way of selecting the is combination and there are no orders to how they are selected
Where
[tex]n=N_a\\\\r=N_t[/tex]
Therefore
[tex]^{27}C_8=\frac{27!}{8!(27-8)!}\\\\^{27}C_8=2220075[/tex]
In conclusion
There are [tex]^{27}C_8=2220075[/tex] different groups of 8 cars are possible when selecting the cars
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