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

`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`