Answer:
b. 70
Step-by-step explanation:
The Binomial Coefficient can be used to calculate the number of ways objects can be arranged.
<u>Binomial Coefficient</u>
![\displaystyle \rm \binom{n}{r} \: = \:^{n}C_{r} = \frac{n!}{r!(n-r)!}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Crm%20%5Cbinom%7Bn%7D%7Br%7D%20%5C%3A%20%3D%20%5C%3A%5E%7Bn%7DC_%7Br%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Br%21%28n-r%29%21%7D)
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:
![\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}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%20%5Cimplies%20%5Cdisplaystyle%20%5Crm%20%5Cbinom%7B8%7D%7B4%7D%20%5C%3A%20%3D%20%5C%3A%5E%7B8%7DC_%7B4%7D%20%26%20%3D%20%5Crm%20%5Cfrac%7B8%21%7D%7B4%21%288-4%29%21%7D%5C%5C%5C%5C%20%26%20%3D%20%5Crm%20%5Cdfrac%7B8%20%5Ctimes%207%5Ctimes%206%5Ctimes%205%5Ctimes%204%5Ctimes%203%5Ctimes%202%5Ctimes%201%7D%7B4%5Ctimes%203%5Ctimes%202%5Ctimes%201%5Ctimes%204%5Ctimes%203%5Ctimes%202%5Ctimes%201%7D%5C%5C%5C%5C%20%26%20%3D%20%5Crm%20%5Cdfrac%7B8%20%5Ctimes%207%5Ctimes%206%5Ctimes%205%7D%7B4%5Ctimes%203%5Ctimes%202%5Ctimes%201%7D%5C%5C%5C%5C%20%26%20%3D%20%5Crm%20%5Cdfrac%7B1680%7D%7B24%7D%5C%5C%5C%5C%20%26%20%3D%20%5Crm%2070%5Cend%7Baligned%7D)
Learn more about the binomial coefficient here:
brainly.com/question/27802390
brainly.com/question/27800539