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What is the number of different messages that can be represented by three a’s and two b’s?1. 72. 83. 94. 10 |
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Answer» Correct Answer - Option 4 : 10 Concept: Suppose a set of n objects has n1 of one kind of object, n2 of a second kind, n3 of a third kind, and so on with n = n1 + n2 + n3 +...+ nk then the number of distinguishable permutations of the n objects is = \(\frac{{{\rm{n}}!}}{{{{\rm{n}}_1}! \times {{\rm{n}}_2}! \times {{\rm{n}}_3}! \ldots \ldots \ldots {{\rm{n}}_{\rm{k}}}!}}\) Given: Three a’s and two b’s
Total number = 3 + 2 = 5 In the set of 5 words has 3 words of one kind and 2 words of the second kind. Therefore, Number of different messages that can be represented by three a's and two b's = \(\frac{{5!}}{{3!2!}} = 10\) |
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