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Home » Divide both sides by 5 to find \( y \): - IQnection

Divide both sides by 5 to find \( y \): - IQnection

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 This is equivalent to counting the number of ways to divide 6 distinct items into 2 non-empty, unlabeled subsets, which is given by:

📌 We subtract the two cases where all models go to one stand (all in one, none in the other), and divide by 2 because the stands are indistinguishable.

📌 Question: A technology consultant is designing a cloud system with 9 servers, 4 of which are high-performance units. If 5 servers are randomly selected for a load-balancing test, what is the probability that at least 3 of the selected servers are high-performance?

📌 Solution: We compute the probability that at least 3 of the selected servers are high-performance, i.e., 3, 4 high-performance servers among the 5 selected.

📌 Total number of ways to choose 5 servers from 9:

📌 3 high-performance and 2 non-high-performance:

📌 4 high-performance and 1 non-high-performance:

📌 Question: A stack of $6n$ cards contains $3n$ red cards and $3n$ blue cards. The cards are shuffled and dealt into 3 equal piles. What is the probability that each pile contains exactly $n$ red cards?

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