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Aptitude Advanced P & C and Probability innovation eBook

Table of Contents Chapter No. Topic 1 Fundamental Principle of Counting Permutations 2.1 Circular Permutations Combinations 3.1 Division of Items into Groups 3.2 Solved Examples Probability 4.1 Classical Definition of Probability 4.2 Total Probability Law 4.3 Baye’s Rule & Miscellaneous solved examples 2 3 4 Page No. 1 3 12 21

Chapter 1: Fundamental Principle of Counting Multiplication: If there are two jobs such that one of them can be completed in m ways, and when it has been completed in any one of these m ways, second job can be completed in n ways, then the two jobs in succession can be completed in m × n ways. Ex. 1. In a class there are 10 boys and 8 girls. The teacher wants to select a boy and a girl to represent the class in a function. In how many ways can the teacher make the selection? Sol. Here the teacher has to perform two jobs. (i) Selecting a boy among 10 boys and (ii) Selecting a girl among 8 girls. The first of these can be performed in 10 ways and the second in 8 ways. Therefore by the fundamental principle of multiplication, the required number of ways is 10 × 8 = 80. Addition: If there are two jobs such that they can be performed independently in m and n ways respectively, 1

then either of the two jobs can be performed in (m + n) ways. Ex. 2. In a class there are 10 boys and 8 girls. The teacher wants to select a boy or a girl to represent the class in a function. In how many ways the teacher can make the selection. Sol. Here the teacher has to perform either of the following two jobs. (i) Selecting a boy among 10 boys or (ii) Selecting a girl among 8 girls. The first of these can be performed in 10 ways and the second in 8 ways. Therefore, by fundamental principle of addition either of the two jobs can be performed in 10 + 8 = 18 ways. Hence the teacher can make the selection of either a boy or a girl in 18 ways. Note: The above principles of counting can be extended to any finite number of jobs. 2

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