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Combinatorial rules of multiplication and addition. Permutations, placements, combinations

Combinatorics in grade 9
Combinatorics studies how to count configurations without listing everything. The sum rule (m+nm+n, disjoint options) and product rule (mnm\cdot n, independent stages) appear often. Then: formulas for permutations Pn=n!P_n=n!, arrangements AnkA_n^k (order matters), and combinations CnkC_n^k (order ignored).
First pick the model: “or” → sum; “and in stages” → product; then permutation, arrangement, or combination
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