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📰 Question: A circular park has 5 distinguishable trees planted around its perimeter and 3 indistinguishable benches to be placed among them. If rotations of the arrangement are considered identical, how many distinct arrangements are possible? 📰 Solution: First, fix one tree to account for rotational symmetry. Since the trees are distinguishable, fixing one eliminates rotational duplicates. The remaining 4 distinguishable trees can be arranged in $4! = 24$ ways around the circle. 📰 Now, we place 3 indistinguishable benches into the 5 gaps between the trees (since the trees form a circle, there are 5 gaps between adjacent trees). The number of ways to distribute 3 indistinguishable benches into 5 distinguishable gaps (with no restriction on how many per gap) is a stars and bars problem: 📰 Savings Vs Checking Account 📰 Cu2 To Cu Reduction Potential 1652674 📰 Manulife Stock Price 📰 Extreme World Recruitment Clash Villarrenal Vs Ovie Stuns Star Ratings 218008 📰 Beta In Yahoo Finance 📰 Top Movers Stock Today 📰 You Wont Believe How These Gold Strappy Heels Transform Your Looktry Them Now 4152297 📰 Sp500 Heat Map Breakdown Why This Chart Is Rewriting The Stock Game 2604721 📰 You Wont Believe Which Pokmon Games Are Poised To Destroy The Nintendo Switch In 2025 4288978 📰 Ed Harris 9073239 📰 Www Verizonwireless Com Pay My Bill 📰 Are Markets Closed For Columbus Day 📰 Ben 10 Alien Names 📰 Lac Stockspotlight Stocktwits Hottest Trade With A 200 Edge This Week 9050040 📰 Logitech K270 Driver