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Permutation and Combination

by Placement FactoryPlacement Factory
Type: NoteCourse: Placement Preparation Specialization: Quantitative AptitudeOffline Downloads: 30Views: 308Uploaded: 2 months ago

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Permutation and Combination by Placement Factory

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Placement Factory
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Permutations & Combinations Extension 1 Mathematics HSC Revision
Multiplication Rule If one event can occur in m ways, a second event in n ways and a third event in r, then the three events can occur in m × n × r ways. Example Erin has 5 tops, 6 skirts and 4 caps from which to choose an outfit. In how many ways can she select one top, one skirt and one cap? Solution: Ways = 5 × 6 × 4
Repetition of an Event If one event with n outcomes occurs r times with repetition allowed, then the number of ordered arrangements is nr Example 1 What is the number of arrangements if a die is rolled (a) 2 times ? 6×6 = 62 (b) 3 times ? 6×6×6 = 63 (b) r times ? 6 × 6 × 6 × ……. = 6r
Repetition of an Event Example 2 (a) How many different car number plates are possible with 3 letters followed by 3 digits? Solution: 26 × 26 × 26 × 10 × 10 × 10 = 263 × 103 (b) How many of these number plates begin with ABC ? Solution: 1 × 1 × 1 × 10 × 10 × 10 = 103 (c) If a plate is chosen at random, what is the probability that it begins with ABC? Solution: 103 263 × 103 = 1 . 263

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