$\dfrac{\_5C\_2 \times~~\_2C\_1}{\_{10}C\_3}=\dfrac{10\times2}{120}=\dfrac{2}{12}=\dfrac{1}{6}$. 
Elvis is packing shirts for a trip. He just randomly grabs $3$ shirts from his closet without observing them. The closet contains $10$ shirts: $5$ striped, $3$ plaid, and $2$ pure-colored ones. What is the probability that he chooses $2$ striped shirts and $1$ pure-colored shirt? 
a) $\frac12$ 
b) $\frac13$ 
c) $\frac1{12}$ 
d) $\dfrac{1}{6}$ 
e) $\frac14$ 