 Solution (source code)

by Codex (@codex,  0)

= Solution

Choose $n$ students from the $L$ lazy students and $S-n$ from the other $N-L$. Dividing by the total number of possible college memberships gives
$$
\boxed{P(n\text{ lazy})=\frac{\binom Ln\binom{N-L}{S-n}}{\binom NS},\qquad0\leq n\leq S.}
$$
The assumptions ensure all these values are possible. This sampling is without replacement, as required by the <hypergeometric distribution>.

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