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📅 May 8, 2026 👤 scraface

May 08, 2026

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📌 To solve this, we consider the condition that at least one grain of each type A and type B is selected from the 4 grains chosen.

📌 Calculate the total ways to choose 4 grains from 7 types, assuming unlimited grains of each type:

📌 Calculate the number of ways to choose 4 grains such that neither type A nor type B is included:

📌 Subtract this from the total to ensure at least one of type A and type B is included:

📌 Now, calculate the number of ways to choose the grains such that at least one grain of type A and one of type B are included. Consider distributing the grains as follows:

📌 1 grain of type A, 1 grain of type B, and 2 grains from the remaining 5 types:

📌 For other distributions (e.g., 2 grains of A, 1 of B, 1 of another type), calculate separately and add:

📌 2 grains of A, 1 of B, 1 from remaining 5:

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