VC2M10AP01
explore counting principles, and factorial notation as a representation that provides efficient counting in multiplicative contexts, including calculations of probabilities
Elaborations
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applying the multiplication principle to problems involving combinations including probabilities relating to sampling with and without replacement, and representing these using tree diagrams
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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}}
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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?
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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
VC2M10AP01 | Mathematics | Mathematics Version 2.0 | Level 10A | Probability