A department store is holding a drawing to give free shopping sprees to two lucky customers. There are $18$ customers who have entered the drawing: $4$ live in the town of Gaston, $8$ live in Pike, and $6$ live in Wells. In the drawing, the first customer will be selected at random, and then the second customer will be selected at random from the remaining customers. What is the probability that both customers selected are Pike residents?
Report your answer as an exact fraction.
My answer The probability that the first customer lives in Pike is
The probability that the second customer lives in Pike is
The probability that both customers selected are Pike residents is
Am I Correct?