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Note for Permutation and Combination - PC by Placement Factory

  • Permutation and Combination - PC
  • Note
  • Quantitative Aptitude
  • Placement Preparation
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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

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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

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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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Factorial Representation n! = n(n – 1)(n – 2)………..3 × 2 × 1 For example 5! = 5.4.3.2.1 Note 0! = 1 Example a) In how many ways can 6 people be arranged in a row? Solution : 6.5.4.3.2.1 = 6! b) How many arrangements are possible if only 3 of them are chosen? Solution: 6.5.4 = 120

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