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📰 Thus, the smallest such integer is $\boxed{5}$.Question: An entomologist studies 5 species of bees, 3 species of wasps, and 2 species of beetles. If she observes one species per day for 10 days, how many distinct observation sequences are possible if species within each category are indistinguishable? 📰 Solution: The problem requires calculating the number of distinct permutations of 10 items where there are 5 identical bees, 3 identical wasps, and 2 identical beetles. The formula for multinomial coefficients applies: 📰 \frac{10!}{5! \cdot 3! \cdot 2!} = \frac{3628800}{120 \cdot 6 \cdot 2} = \frac{3628800}{1440} = 2520 📰 Slides Background 7665158 📰 How Mermaid Hoco Dresses Elevate Your Wardrobe Secret Styles Youll Love 8599923 📰 Roblox Seal Game 4046760 📰 Hemorrhagic Splinters In Nails 1855129 📰 Dilmil Shocking Benefits That Will Change The Way You Eat Forever 2949539 📰 Citi Aa Card 5513638 📰 A Cylindrical Tank Has A Radius Of 3 Meters And A Height Of 5 Meters If The Tank Is Filled With Water At A Rate Of 2 Cubic Meters Per Minute How Long Will It Take To Fill The Tank Completely 4140255 📰 Rd Shell Share Price 7266339 📰 Define Repast 6819986 📰 Meadowood Napa Valley 562483 📰 Condos Games Roblox 8889113 📰 No Overtime Tax Avoided Heres The Insider Law Thats Changing Everything 891799 📰 Gameonline Impossible Discover The Champions Proven To Dominate 8058752 📰 Waiting In A Queue For Fortnite 1564602 📰 Alan Wake Remastered Walkthrough 2691676