There are 7 people fishing at Lake Connor: 5 have fishing licenses, and 2 do not. An inspector chooses two of the people at random. What is the probability that the first person chosen has a license and the second one does not? Write your answer as a fraction in simplest form.
There is a $\dfrac{5}{7}$ probability that the first person chosen has a license. Then, there are 6 remaining people, 2 of whom do not have a license. So the probability that the second person chosen does not have a license given that the first did is $\dfrac{2}{6} = \dfrac{1}{3}$. Therefore, the probability that the first person has a license and the second one does not is $\dfrac{5}{7} \cdot \dfrac{1}{3} = \boxed{\frac{5}{21}}$.
