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Home » We start with the equation for population growth: - American Beagle Club

We start with the equation for population growth: - American Beagle Club

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 An AI startup has 7 engineers, and the company wants to form a 4-member innovation team. If at least 2 engineers must specialize in machine learning (and there are 4 such specialists), how many valid teams can be formed?

📌 We consider cases:

📌 Case 1: 2 ML + 2 others: \(\binom{4}{2} \times \binom{3}{2} = 6 \times 3 = 18\)

📌 Case 2: 3 ML + 1 other: \(\binom{4}{3} \times \binom{3}{1} = 4 \times 3 = 12\)

📌 Case 3: 4 ML: \(\binom{4}{4} = 1\)

📌 Total: \(18 + 12 + 1 = 31\)

📌 A technology firm uses a 6-digit security code where each digit is from 0–9, but the first digit cannot be 0. How many valid codes are possible?

📌 First digit: 9 choices (1–9). Each of the remaining 5 digits: 10 choices. Total: \(9 \times 10^5 = 900,000\).

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