Answer:
b. 70
Step-by-step explanation:
The Binomial Coefficient can be used to calculate the number of ways objects can be arranged.
Binomial Coefficient
[tex]\displaystyle \rm \binom{n}{r} \: = \:^{n}C_{r} = \frac{n!}{r!(n-r)!}[/tex]
The exclamation mark "!" placed after a number means factorial and indicates to multiply all whole numbers from the given number down to 1.
Example: 4! = 4 × 3 × 2 × 1
The Binomial Coefficient gives us the number of ways of picking "r" unordered outcomes from "n" possibilities.
As there are 8 friends ⇒ n = 8.
As each car takes 4 friends ⇒ r = 4.
Substitute these values into the formula:
[tex]\begin{aligned} \implies \displaystyle \rm \binom{8}{4} \: = \:^{8}C_{4} & = \rm \frac{8!}{4!(8-4)!}\\\\ & = \rm \dfrac{8 \times 7\times 6\times 5\times 4\times 3\times 2\times 1}{4\times 3\times 2\times 1\times 4\times 3\times 2\times 1}\\\\ & = \rm \dfrac{8 \times 7\times 6\times 5}{4\times 3\times 2\times 1}\\\\ & = \rm \dfrac{1680}{24}\\\\ & = \rm 70\end{aligned}[/tex]
Learn more about the binomial coefficient here:
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