Question

A class is attended bynsophomores,njuniors, andnseniors. In how many ways canthese students formngroups of three people each if each group is to contain asophomore, a junior, and a senior?

Answer 1

Answer:

$n^3$

Step-by-step explanation:

The number of ways of choosing $r$ objects from $n$ is $\binom{n}{r}=\frac{n!}{r!(n-r)!}$. Specifically, $\binom{n}{1}=n$.

Since there are $n$ sophomores, there are $n$ ways of picking 1 sophomore from $n$.

By the same reasoning, there are $n$ ways of picking 1 junior and $n$ ways of picking 1 senior.

The total number of ways of picking 1 sophomore, 1 junior and 1 senior = $n\times n\times n=n^3$