InterviewSolution
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InterviewSolution
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One mapping is selected at random from all the mappings of the set A = {1, 2, 3, ….., n) into itself. The probability that the mapping selected is one to one isA. \(\frac{1}{n^2}\)B. \(\frac{1}{n!}\)C. \(\frac{(n-1)!}{n^{n-1}}\) D. none of these |
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Answer» We know that the no of mapping from a set A to same set containing n elements = nn As each element have n options to be mapped with n elements. For mapping selected to be one to one, for first element we have n options ,for second we have n-1 options an so on… ∴ total such mappings = n × (n-1)× (n-2)× … = n! ∴ P(mapping is one to one) = \(\frac{n!}{n^n}\) = \(\frac{n(n-1)!}{n^n}\) = \(\frac{(n-1)!}{n^n-1}\) Our answer matches with option (c) ∴ Option (c) is the only correct choice |
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