explore counting principles, and factorial notation as a representation that provides efficient counting in multiplicative contexts, including calculations of probabilities
Elaborations
applying the multiplication principle to problems involving combinations including probabilities relating to sampling with and without replacement, and representing these using tree diagrams
understanding that a set with n elements has 2n different subsets formed by considering each element for inclusion or not in combination, and that these can be systematically listed using a tree diagram or a table; for example, the set {a, b, c} has 23 = 8 subsets which are { ∅, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}}
using the definition of n! to represent and calculate in contexts that involve choices from a set; for example, how many different combinations of 3 playing cards from a pack? How many if the suits are ignored? How many with and without replacement?
performing calculations on numbers expressed in factorial form, such as n!r! to evaluate the number of possible arrangements of n objects in a row, r of which are identical; for example, 5 objects, 3 of which are identical, can be arranged in a row in 5!3!=5×4×3×2×13×2×1=20 different ways
Code
VC2M10AP01
Curriculum resources and support
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