Question: 2019 Winter Midterm - 8
Let $n \geq 4$ be an integer. What does
$$
3 \cdot { n\choose 3} + 6n \cdot {n \choose 2} + n^3
$$
count?
(a)
The number of ways to choose an ordered triple
<p style="text-align: center; margin: 0.5rem 0;">
(beer bottle, cider bottle, wine bottle)
</p>
in a set consisting of $n$ beer bottles, $n$ cider bottles, and $n$ wine bottles.
(b)
The number of ways to choose a 3-element subset of a set consisting of $n$ beer bottles, $n$ cider bottles, and $n$ wine bottles.
(c)
The number of ways to choose 3 elements (with repetitions allowed) in a set consisting of $n$ beer bottles, $n$ cider bottles, and $n$ wine bottles.
(d)
None of the above.