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Home » The area $ A $ of the circular base is: - Coaching Toolbox

The area $ A $ of the circular base is: - Coaching Toolbox

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 #### 17, 18Question: A palynologist is analyzing the distribution of pollen samples from 5 different plant species labeled A through E. If each sample must be analyzed exactly once and the order of analysis matters, how many distinct sequences are possible if species A must be analyzed before species B?

📌 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:

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