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Home » Kiwi Surprise: Dogs Can Eat It—but Only in Tiny Amounts! Here’s Why! - IQnection

Kiwi Surprise: Dogs Can Eat It—but Only in Tiny Amounts! Here’s Why! - IQnection

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Solution: Let $n = 4$, so the deck has $3n = 12$ cards labeled from 1 to 12. We want the probability that the sum of 3 randomly drawn distinct cards is divisible by 3.

📌 We analyze residues modulo 3. The numbers from 1 to 12 modulo 3 fall into three residue classes:

📌 Total favorable: $4 + 4 + 4 + 64 = 76$

📌 Question: A pharmacologist is testing combinations of 4 experimental compounds from a pool of 8, where 3 are neuroprotective and 5 are anti-inflammatory. If the selection includes at least one compound from each category, how many such combinations are possible?

📌 We subtract the cases that violate the at least one from each category condition:

📌 Also exclude the case where no neuroprotective compound is chosen (already included), and no anti-inflammatory — also impossible.

📌 So only invalid case is selecting all 4 from anti-inflammatory: 5 ways.

📌 Thus, valid combinations: $70 - 5 = 65$

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