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We can compute this by summing over all possible $7$-element subsets of the $10$ weights, then counting the number of permutations of those $7$ weights where the maximum is in the last position (feature $7$).
Question: An epidemiologist is modeling disease spread using a population of $12$ individuals, where $5$ are initially infected and $7$ are susceptible. If the infection spreads only through random pairing—each day, one infected person transmits to one susceptible person—what is the probability that, after all possible transmissions until no new infections are possible, exactly $9$ individuals have been infected by the end?
We begin with $5$ infected and $7$ susceptible individuals. The transmission rule: each day, an infected person infects one susceptible (via a random pairing, assume all infection pairs are equally likely over time, but the process stops when no new infections can occur). However, since only $5$

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