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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?

User Nayda
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1 Answer

4 votes

Answer:


n^3

Explanation:

The number of ways of choosing
r objects from
n is
\binom{n}{r}=(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* n* n=n^3

User Ivangtorre
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