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📰 \binom{7}{4} \cdot \binom{4}{2} \cdot 4! = 35 \cdot 6 \cdot 24 = 5040. 📰 But if the "order" refers only to the application of the operation (i.e., 2 positions are distinct for pumping), the count is $ \binom{7}{4} \cdot \binom{4}{2} \cdot \frac{4!}{2!} = 35 \cdot 6 \cdot 12 = 2520 $. Clarifying the problem's intent, the most plausible interpretation leads to $\boxed{2520}$. 📰 Question: A nanotechnology engineer is designing a solar-powered water harvesting system with 5 identical microfilters. How many distinct ways can 8 unique water source samples be distributed into the filters if each filter can hold any number of samples? 📰 Chuck Steak That Cooks In Minutesthis Secret Will Shock You 6387249 📰 Breaking News The Obelisks Dark Legacy Revealedarchaeologists Finally Solve The Mystery 9784426 📰 Hotel Ciragan 2708890 📰 Inside The Tourney Machine The Game Changer Thats Taking Esports By Storm 3538256 📰 Christopher Landon 8439295 📰 City Of Longview Water Dept 1796252 📰 Why This 2006 Toyota Tundra Was Secretly Built For Off Road Legendsgiving Gandhi A Run For His Durable Throne 8079103 📰 You Wont Believe How Fire Red Pokdex Unlocks Hidden Early Pokmon Powers 279561 📰 Boca Raton Florida 8338261 📰 When Does Downtime End For Fortnite 5489093 📰 Unlock Your Glow The Secret Skincare Headband You Need To Try Tonight 8993949 📰 Harry Potter Half Blood Prince Cast 8094143 📰 Chicken Coop Kit 1347936 📰 Verizon First Responders Discount 3189718 📰 Shocking Blue Eggs You Wont Believe What Could Be Inside This Rare Ova 2663230