Suppose 2 distinct integers are chosen from 1 through 9, inclusive.  What is the probability that they are both odd?
Let's consider an `outcome' to be a choice of 2 numbers without regard to order.  There are $\binom{9}{2} = 36$ ways to choose 2 numbers from our set of 9 if we don't care about order.  There are $\binom{5}{2} = 10$ ways to choose 2 numbers from the 5 odd numbers without regard to order.  Therefore, the probability is $\frac{10}{36} = \boxed{\frac{5}{18}}$.