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Home » The Secret to Eco-Friendly Cozy Living Starts with This Chair and Ottoman Duo! - Network4

The Secret to Eco-Friendly Cozy Living Starts with This Chair and Ottoman Duo! - Network4

📅 May 21, 2026 👤 scraface

May 21, 2026

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📌 A science policy analyst evaluates funding allocations across 6 scientific disciplines. Each of 4 proposed grants is independently assigned to one discipline. What is the probability that exactly 2 disciplines receive 2 grants each, and the remaining 2 disciplines receive none?

📌 First, compute the total number of ways to assign 4 grants to 6 disciplines:

📌 Now, count the number of favorable assignments where exactly 2 disciplines receive 2 grants each.

📌 Step 1: Choose 2 disciplines out of 6 to receive the grants:

📌 Step 2: Assign the 4 distinct grants such that each of the 2 chosen disciplines gets exactly 2 grants. The number of ways to partition 4 distinguishable grants into two groups of 2 is:

📌 But since the disciplines are distinguishable, we assign which pair goes to which discipline: we choose 2 grants for first discipline, and the remaining 2 go to the second:

📌 So for each pair of disciplines, there are 6 valid assignments.

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