Exercise 3.27

$X$ is not Binomial becuase the outcome of a card is not independent of the previous cards’ outcomes. For instance, if the first $n-1$ cards match, then the probability of the last card matching is $1$.

The Hypergeometric story requires sampling from two finite sets, but the matching cards isn’t a set of predetermined size, so the story doesn’t fit.

where $!(n-k)$ is a subfactorial.