Question: 2014 Winter Final - 13
Let $A = \{1,2,3,\dots,100\}$. Let $x$, $y$, and $z$ be elements in $A$ that are chosen independently
and uniformly at random. What is the probability that $x = y = z$?
(a)
$\frac{1}{100 \cdot 100}$
(b)
$\frac{1}{100 \cdot 99}$
(c)
$\frac{1}{100}$
(d)
$\frac{1}{{100 \choose 2}}$