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📰 Question: If a historian selects 3 manuscripts at random from a collection of 15, where 5 are from the 18th century, what is the probability that all 3 selected are 18th-century manuscripts? 📰 Solution: The number of ways to choose 3 18th-century manuscripts is $inom{5}{3}$. Total ways to choose 3 manuscripts from 15 is $inom{15}{3}$. The probability is $rac{inom{5}{3}}{inom{15}{3}} = rac{10}{455} = rac{2}{91}$. $oxed{\dfrac{2}{91}}$Question: If the combined population of two marine mammal species in a region is 10 and the sum of their squared populations is 50, find the sum of their cubes. 📰 Solution: Let the populations be $ a $ and $ b $. Given $ a + b = 10 $ and $ a^2 + b^2 = 50 $. First, compute $ ab $ using $ (a + b)^2 = a^2 + 2ab + b^2 $. Substituting, $ 100 = 50 + 2ab $, so $ ab = 25 $. The sum of cubes is $ a^3 + b^3 = (a + b)^3 - 3ab(a + b) = 1000 - 3 \cdot 25 \cdot 10 = 1000 - 750 = oxed{250} $. 📰 The Descent Part Two Fans Demand Answerswhat Happened Next Will Shock You 8221192 📰 Ui For Windows 10 9623569 📰 Sepsis The Contagious Error You Never Knew Abouta Deadly Misconception 1788425 📰 What Burger Joint Reinvented Breakfast Forevershocking Companys All New Menu Revealed 1463457 📰 Space Waves Just Explodedthis Shocking Event Changed Astronomy Forever 3235217 📰 Film Cold Creek Manor 1812254 📰 Costco Option Chain 7200361 📰 Play These Free Defense Tower Games And Save Big This Month 6802706 📰 Find Your Shade With These Ignite Your Mind Would U Rather Dilemmas Try Them Now 2159425 📰 Ala Moana Beach Park 1839377 📰 Stop Stressingoracle Support Contact Details You Need Right Now 2586058 📰 How John Carmack Rewrote Gamingand What He Kept Hidden 8256860 📰 Online Texas Hold Em Free 8504063 📰 Coreweave Yahoo The Revolutionary Tech Manipulated By Big Tech Giants 5862350 📰 From Zero To Hero How Playing Online Games Unlocked Hidden Power In Millions 7187661