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NSWMaths Extension 1Quick questions
Combinatorics (ME-A1)
Quick questions on Using counting in probability: P = favourable/total with both counts from permutations and combinations, plus complement, cases and inclusion-exclusion for committees, card hands, digit strings and replacement draws
6short 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 selection probabilities with combinations?Show answer
The commonest equally likely model is a random selection: a committee, a team, a hand, a handful of discs. Order does not matter, so the sample space is a combination, and the favourable count is a combination (or a product of combinations from separate pools). The whole pattern is
What are card-hand probabilities?Show answer
A standard pack has cards in suits of . A poker-style hand of cards is an unordered selection, so the sample space is
What is "At least one" by the complement?Show answer
"At least one" almost always fragments into several cases ("exactly one", "exactly two", ...), so it is far shorter to count the complement, "none", and subtract its probability from :
What is exactly of one suit?Show answer
For exactly hearts, choose of the hearts and the other from the non-hearts:
What are a specified split across two suits?Show answer
For spades and hearts, choose from each suit and multiply:
What is all five of one suit?Show answer
Any one of the suits supplies all cards, so multiply by :
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