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NSWMaths Extension 1Quick questions
Combinatorics (ME-A1)
Quick questions on Circular arrangements: why n distinct objects around a circle give (n-1)!, the block method for groups and couples, alternating patterns, 'not together' via the complement, and necklaces/bracelets dividing by 2 for reflection
3short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.
What are alternating patterns?Show answer
A favourite restriction is alternating two types around a circle, boys and girls, odds and evens, two colours, in strict order. With objects of each type, the clean method is: seat one type first as a circle, then slot the other type into the gaps.
What is using circular counts in probability?Show answer
Once you can count circular arrangements, probabilities follow from , with both counts done by the methods above. For example, three Tasmanians, three New Zealanders and three Queenslanders ( people) sit at random around a round table; the chance the three state-groups each sit together is
What is verifying a small case by listing?Show answer
Whenever a circular count is small, you can list the genuinely different arrangements to check the formula, the discipline being to fix one object so you never write a rotation twice. Take people around a table. The formula gives $(4-1)! = 3!
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