1 .
Let $n \geq 2$ be an integer. You are given $n$ beer bottles $B_1,B_2,\dots,B_n$ and two cider
bottles $C_1$ and $C_2$. You choose a uniformly random 3-element subset of the set of these $n+2$
bottles. Define the random variable $X$ to be
- X = the number of cider bottles in the chosen subset.
(a)
$\frac{2 {{n}\choose{2}} + n - 1}{{{n+2}\choose{3}}}$
(b)
$\frac{2 {{n}\choose{2}} + n + 1}{{{n+2}\choose{3}}}$
(c)
$\frac{2 {{n}\choose{2}} + n}{{{n+2}\choose{3}}}$
(d)
$\frac{2 {{n}\choose{2}} + 2n}{{{n+2}\choose{3}}}$