Mutual Funds Top Picks That Could Make Your Savings Grow Overnight!

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How mutual funds can convert your small savings into big wealth
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Question: A hydrologist is modeling groundwater flow through 7 distinct soil layers. How many distinct sequences of 4 layers can be selected and ordered for analysis if the operation "pump water" is applied to exactly 2 of them?
Solution: First, choose 4 distinct layers from 7, which is $ \binom{7}{4} = 35 $. Then, select 2 of these 4 layers to apply the "pump water" operation, which can be done in $ \binom{4}{2} = 6 $ ways. The remaining 2 layers are analyzed without the operation, and the sequence of 4 layers is ordered, giving $ 4! = 24 $ permutations. However, since the operation affects only the selection (not the order of non-pump layers), the total is:
\binom{7}{4} \cdot \binom{4}{2} \cdot 4! = 35 \cdot 6 \cdot 24 = 5040.

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