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Home » Shocked You Didn’t Know These Teenage Mutant Ninja Turtle Names First! - inBeat

Shocked You Didn’t Know These Teenage Mutant Ninja Turtle Names First! - inBeat

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 A STEM student builds a robot with a sequence of gears. If each gear has 10 teeth and the sequence consists of 3 gears in series, how many teeth are engaged when the gears rotate together?

📌 In a series, only the first gear’s teeth engage with the second, and the second’s engage with the third. Since teeth interlock pairwise, the total engaged teeth are those of two gears: \(10 + 10 = 20\).

📌 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: \(18 + 12 + 1 = 31\)

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