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Home » \sum_\substacka=1\\b=0\\c=0^2,1,1 2^a \cdot 3^b \cdot 5^c - jntua results

\sum_\substacka=1\\b=0\\c=0^2,1,1 2^a \cdot 3^b \cdot 5^c - jntua results

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 \frac{5!}{2} = \frac{120}{2} = 60

📌 \boxed{60}

📌 Question: A wildlife conservation genomics researcher is tracking 6 distinct mountain gorillas for genetic sampling. If the researcher plans to randomly select 3 gorillas to tag on Monday and the remaining 3 on Tuesday, what is the probability that two specific gorillas, Gorilla X and Gorilla Y, are both tagged on the same day?

📌 We begin by computing the total number of ways to divide 6 distinct gorillas into two groups of 3, where the order of the days (Monday and Tuesday) matters. This is simply:

📌 Now, we count the number of favorable outcomes where Gorilla X and Gorilla Y are both on the same day. There are two cases:

📌 Case 1:** Both X and Y are on Monday.

📌 Then we must choose 1 more gorilla from the remaining 4 to join them:

📌 \binom{4}{1} = 4

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