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Home » $S_5 = 7 + 4 + 2 = 13$ - DNSFLEX

$S_5 = 7 + 4 + 2 = 13$ - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 5Question: A programmer is developing an AI model that classifies medical images into 4 categories: tumor, inflammation, normal, and stroke. If the model is tested on a dataset of 10 images, and each image is independently classified into one of the 4 categories, how many different classification outcomes are possible such that exactly 3 images are labeled as "tumor", 2 as "inflammation", 4 as "normal", and 1 as "stroke"?

📌 Solution: We are asked to count the number of distinct ways to assign 10 independently classified images into 4 categories with fixed counts: 3 as tumor, 2 as inflammation, 4 as normal, and 1 as stroke. This is a multinomial coefficient problem.

📌 The number of such classification outcomes is given by:

📌 \frac{10!}{3! \cdot 2! \cdot 4! \cdot 1!}

📌 We compute step-by-step:

📌 $10! = 3628800$

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