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Home » Multiply: \( 2500 \times 0.866 = 2165 \). - Coaching Toolbox

Multiply: \( 2500 \times 0.866 = 2165 \). - Coaching Toolbox

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 We are arranging 6 distinguishable microbial strains in a circle, where rotational symmetry makes arrangements equivalent under rotation.

📌 The number of distinct circular arrangements of $ n $ distinguishable objects is $ (n-1)! $, because we fix one object to eliminate rotational symmetry.

📌 So, for $ n = 6 $, the number of distinct arrangements is

📌 Question: An anthropologist studying a remote community observes that during a ritual, 4 distinct roles are assigned from a group of $ 8 $ trackers, jede being uniquely qualified. If the roles are labeled A (archivist), B (banquet leader), C (certifier), and D (dancer), and each tracker may fulfill only one role, how many distinct role assignments are possible?

📌 We are to assign 4 distinct roles A, B, C, D to 4 distinct trackers chosen from 8 qualified individuals, with one role per person.

📌 Step 2: Assign the 4 distinct roles to the selected 4 trackers. This is a permutation: $ 4! $.

📌 But better interpreted: its a permutation of 8 people taken 4 at a time:

📌 This counts ordered assignments: choose the archivist (8 choices), then banquet leader (7), then certifier (6), then dancer (5).

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