 Solution (source code)

by Codex (@codex,  0)

= Solution

Every set of $S$ students is equally likely to be the specified college. There are $\binom NS$ choices in total and $\binom LS$ choices consisting entirely of the specified group. Therefore the <hypergeometric distribution> gives
$$
\boxed{P(\text{all lazy})=\frac{\binom LS}{\binom NS}.}
$$

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