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Random pick problem

Source: AHSME 1986 problem 22

October 1, 2011
probabilityAMC

Problem Statement

Six distinct integers are picked at random from {1,2,3,…,10}\{1,2,3,\ldots,10\}. What is the probability that, among those selected, the second smallest is 33?
<spanclass=′latex−bold′>(A)</span> 160<spanclass=′latex−bold′>(B)</span> 16<spanclass=′latex−bold′>(C)</span> 13<spanclass=′latex−bold′>(D)</span> 12<spanclass=′latex−bold′>(E)</span> none of these <span class='latex-bold'>(A)</span>\ \frac{1}{60}\qquad<span class='latex-bold'>(B)</span>\ \frac{1}{6}\qquad<span class='latex-bold'>(C)</span>\ \frac{1}{3}\qquad<span class='latex-bold'>(D)</span>\ \frac{1}{2}\qquad<span class='latex-bold'>(E)</span>\ \text{none of these}
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