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Home » Now, ensure each has a clear question and solution. Also, check LaTeX formatting. - Moon Smoking

Now, ensure each has a clear question and solution. Also, check LaTeX formatting. - Moon Smoking

📅 May 15, 2026 👤 scraface

May 15, 2026

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📌 But since the assignment must preserve the maximal total (which is forced by using the $7$ largest weights), and the condition specifies only that the highest feature has the largest weight, we must count the number of permutations of $7$ weights chosen from $10$, where the largest of the selected $7$ is assigned to position $7$ (the highest-indexed feature).

📌 Among these $7$ selected weights, identify the largest one. This weight must be assigned to the feature with the highest index (feature $7$) to satisfy the condition.

📌 The remaining $6$ selected weights (which include $6$ smaller ones) can be assigned to the first $6$ features in any order.

📌 Thus, for each such 7-weight subset that includes the maximum possible weight (but we dont fix which, so we must allow any subset), but to count valid assignments satisfying the constraint, we fix the structure:

📌 The largest available weight in the chosen set must go to feature $7$.

📌 So we count all injective assignments of $7$ distinct weights from $10$ to $7$ features, such that the maximum weight among the $7$ is assigned to feature $7$.

📌 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?

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