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Home » $ \sin(-2\pi/9) = -\sin(40^\circ) $ - wispro

$ \sin(-2\pi/9) = -\sin(40^\circ) $ - wispro

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 To solve this, we begin by considering all permutations of the 5 species. Since each species is analyzed exactly once and order matters, the total number of unrestricted permutations is:

📌 Now, we impose the condition that species A must be analyzed before species B. In any permutation of the 5 species, for every pair A and B, A appears either before B or after B, with equal likelihood. Thus, exactly half of all permutations satisfy the condition that A comes before B.

📌 So, the number of valid sequences is:

📌 \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:

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