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Home » Solving the quadratic equation \( n^2 + n - 420 = 0 \): - Professionaloutdoormedia

Solving the quadratic equation \( n^2 + n - 420 = 0 \): - Professionaloutdoormedia

📅 May 14, 2026 👤 scraface

May 14, 2026

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📌 Alternatively, we use generating functions. The generating function for each vegetable type is:

📌 So the total generating function is:

📌 Question: A data scientist is analyzing the genetic variability in a population of 100 individuals, where 60 have gene variant A, 40 have variant B, and 20 have both. If a random sample of 10 individuals is selected, what is the probability that exactly 5 have variant A and exactly 4 have variant B (allowing overlap)?

📌 We are selecting 10 individuals from 100, where:

📌 We want the number of samples of size 10 with:

📌 Exactly 5 with A (either only A or both)

📌 Exactly 4 with B (either only B or both)

📌 From $ a = 5 - c $, $ b = 4 - c $, substitute into total:

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