InterviewSolution
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InterviewSolution
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One of the most important techniques of counting is the principle of exclusion and inclusion. Let A_(1),A_(2)….A_(m) be m sets and n(A_i) represents the cordinality of the set A, (the number of elements in the set A_i), then according to the principle of exclusion and inclusion.sum_(i=1)^(m)n(A_i)-sum_( i ne j) n (A_i cap A_j)+sum_(i ne j ne k) n(A_(i) cap A_(j) cap A_(k))-.....+(-1)^(n)n(A_(1) cap A_(2) cap ....cap A_(m)). In particular , if A,B,C are three sets, then n ( A cap B cap C ) =n(A)+n(B)+n(C ) -n(A cap B)- n(B cap C)- n(C cap A)+n(A cap B cap C). Principle of exclusion and inclusion must be applied whenever there is a chance of repeated counting of some of the samples. The number of numbers from 1 to 100, which are neither divisible by 3 nor by 5 nor by 7 is . |
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Answer» 67 |
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