Repeating the same pair of dice values

Two fair six-sided dice are thrown and the two numbers are noted. Both dice are then thrown a second time. What is the probability that the second throw produces the same pair of numbers as the first (in either order)?

$\tfrac{11}{216}$. If the first throw is a double (probability $\tfrac16$), the repeat needs that exact double, probability $\tfrac1{36}$. If it shows two different values (probability $\tfrac56$), either order works, probability $\tfrac2{36}$. Total $\tfrac16\cdot\tfrac1{36}+\tfrac56\cdot\tfrac1{18}=\tfrac{11}{216}$.