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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? 📰 Effortless Elegance Master The Perfect 3 Ingredient Slow Cooker Pot Roast 8281406 📰 Watch Your Mail Delivery Skyrocket Print Envelopes With Just One Click 6181887 📰 You Wont Believe Whats Happening In Saas News Todayshock The Industry 2168170 📰 Why This Burned Roast Is The Hottest Secret In Kitchen Reviewstry It Now 9989089 📰 Prison Architect 5160043 📰 Arrange The Colors Within The Block 4662882 📰 Gitlab Stock Update Could It Rise Over 100 Dont Miss This Market Bomb 3954891 📰 Hyatt Regency Resort And Spa Scottsdale Arizona 3022526 📰 Finally The Simple Way To Create An Xbox Account Watch In Seconds 8870098 📰 Why All The Hype About Fiber Linenthe Truth Behind Its Luxurious Rise 5078104 📰 Cinema Cafe Edinburgh Locks Hearts The Secret Spot Where Films Come Alive 2295875 📰 Reverse Charades The Shocking Twist Everyones Too Afraid To Try 5757793 📰 This Minecraft Map Seed Will Take Your Mining Game To Earns Thousands Of Hidden Resources 467893 📰 Edward Herrmann Revealed The Starr Roles That Made His Voice Unforgettable In Movies And Tv 6924064 📰 X 44 135994