1986 AHSME Problem 22

Six distinct integers are picked at random from \{1,2,3,\ldots,10\}. What is the probability that, among those selected, the second smallest is 3?

\textbf{(A)}\ \frac{1}{60}\qquad \textbf{(B)}\ \frac{1}{6}\qquad \textbf{(C)}\ \frac{1}{3}\qquad \textbf{(D)}\ \frac{1}{2}\qquad \textbf{(E)}\ \text{none of these}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.