three out of seven students in the cafeteria line are chosen to answer survey questions. how many different…

Explanation:

Step1: Recall combination formula

The combination formula is ${n}C{r}=\frac{n!}{(n - r)!r!}$, where $n$ is the total number of items, and $r$ is the number of items to be chosen. Here $n = 7$ and $r=3$.

Step2: Calculate factorial values

$n!=7!=7\times6\times5\times4\times3\times2\times1$, $(n - r)!=(7 - 3)!=4!=4\times3\times2\times1$, $r!=3!=3\times2\times1$. Then ${7}C{3}=\frac{7!}{(7 - 3)!3!}=\frac{7\times6\times5\times4!}{4!\times3\times2\times1}$.

Step3: Simplify the expression

The $4!$ terms in the numerator and denominator cancel out. We get $\frac{7\times6\times5}{3\times2\times1}=\frac{210}{6}=35$.

Answer:

B. 35