Ch 6 develops systematic counting techniques: the fundamental counting principle, permutations (arrangements where order matters), and combinations (selections where order doesn't matter).
If one task can be done in m ways and another in n ways, both tasks can be done in m × n ways (multiplication). If either task is done, total ways = m + n (addition).
A permutation is an arrangement. nPr = n!/(n−r)! = number of ways to arrange r items from n. For n items: n! arrangements. With repetition: nʳ ways.
A combination is a selection (order doesn't matter). nCr = n!/[r!(n−r)!]. nCr = nPr/r!. Key properties: nC0 = nCn = 1, nCr = nC(n−r), nCr + nC(r−1) = (n+1)Cr.
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Permutation: arrangement where ORDER matters (e.g., seating arrangements, passwords). Combination: selection where order does NOT matter (e.g., choosing a committee, selecting cards). nPr ≥ nCr always.
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