Enumeration

Counting without listing — and the one topic that is entirely new at this level.

• An Overview — the big idea, the key formulae, and how to tell permutations from combinations

The specification statements

• EN1 · The Binomial Expansion — Pascal’s triangle, the binomial coefficients, and expanding (a + b)ⁿ
• EN3 · The Product Rule for Counting — multiplying choices, arrangements and factorials
• EN4 · Permutations — ordered selections, and the nPr notation
• EN5 · Combinations — unordered selections, and the nCr notation
• EN2 · Representing Outcomes — tree diagrams, two-way tables and Venn diagrams
• EN6 · Counting in Probability — the binomial distribution, and “at least” problems

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Each page has step-by-step notes, several worked examples, a quick-reference grid and ten practice questions with fully worked solutions.