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counting with triangle inequality

Source: LIMIT 2019 CBS1 P11

April 28, 2021
combinatoricsgeometrytriangle inequalityinequalities

Problem Statement

Let S={1,2,…,10}S=\{1,2,\ldots,10\}. Three numbers are chosen with replacement from SS. If the chosen numbers denote the lengths of sides of a triangle, then the probability that they will form a triangle is: <spanclass=′latex−bold′>(A)</span> 101200<span class='latex-bold'>(A)</span>~\frac{101}{200} <spanclass=′latex−bold′>(B)</span> 99200<span class='latex-bold'>(B)</span>~\frac{99}{200} <spanclass=′latex−bold′>(C)</span> 12<span class='latex-bold'>(C)</span>~\frac12 <spanclass=′latex−bold′>(D)</span> 110200<span class='latex-bold'>(D)</span>~\frac{110}{200}
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