I randomly pick an integer between 1 and 10 inclusive. What is the probablility that I choose a p such that there exists an integer q so that p and q satisfy the equation pq-2p-2q=2? Express your answer as a common fraction.
Using Simons favorite factoring trick gets us (p-2)(q-2)=6 so (p-2) can be either 1,2,3, or 6 meaning p is 3,4,5, or 8. 2/5