There are $2\times6=12$ different combinations. The product of two numbers is smaller than $6$ will be $5\times1$. Thus, the probability is $\frac 1{12}$. 
Two tiles numbered $5$ and $6$ are turned face down, respectively. One tile is turned up at random, and throw a die to get a number from $1$ to $6$. What is the probability that the product of the numbers on the tile and the die is smaller than $6$? 
A) $\frac {1}{2}$ 
B) $\frac {1}{3}$ 
C) $\frac {1}{4}$ 
D) $\frac {1}{6}$ 
E) $\frac {1}{12}$ 