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📰 Solution: The probability of selecting no quantum dots (all nanotubes) is $\frac{\binom{7}{3}}{\binom{12}{3}} = \frac{35}{220}$. The complement gives the probability of at least one quantum dot: $1 - \frac{35}{220} = \frac{185}{220} = \frac{37}{44}$. \boxed{\dfrac{37}{44}} 📰 Question: A venture capitalist evaluates 9 clean energy startups, 4 of which are solar-based. If 5 startups are chosen randomly, what is the probability that exactly 3 are solar-based? 📰 Solution: The total number of ways to select 5 startups is $\binom{9}{5}$. The favorable case is $\binom{4}{3} \cdot \binom{5}{2}$ (3 solar and 2 non-solar). Thus, the probability is $\frac{4 \cdot 10}{126} = \frac{40}{126} = \frac{20}{63}$. \boxed{\dfrac{20}{63}}### Question 1 📰 Gay Rights Unleashed The Surprising Truth Behind The Fight For Equality 7959207 📰 Think Apps Can Track Time Try This Digital Clock App That Applies Smart Precision 5484846 📰 The Secret Fix For Visual Studio Errors Found Visual C Redistributable You Can Download Today 4132606 📰 Instagram Story Virwer 760701 📰 Free Java 6 Jdk Downloadthe Fast Way To Old Java Development 1692063 📰 Nine Nine Tv Show 3059586 📰 How Many More Infections Are Prevented Daily By A 90 Effective Vaccine On 10000 People Compared To An 85 Effective One On 15000 If Exponential Growth Is Ignored But Thats Artificial 2334775 📰 From Childhood Nostalgia To Heart Pounding Dramaunlock The True Mystery Of Digimon Adventure 6893105 📰 This Pink Top Is The Ultimate Secret Advertising Everythingfind Out What Its Hiding 5157854 📰 Live Tv Streaming Apps 2856995 📰 Abbey Gate Bombing 4261623 📰 Is Fortnite Getting Banned 7723061 📰 Flights From San Diego To Las Vegas 7968752 📰 This Simple Excel Hack Boosts Your Future Value Calculation By 300 1676793 📰 Naruto Shippuden 2 Game 5310337