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.
+133 pq-2p-2q-2=0
p(q-2)-2q-2=0
p(q-2)-2q+4 = 6
p(q-2)-2(q-2)=6
(p-2)(q-2)=6
Factors of 6: ±1,2,3,6
According to these factors, (p,q) = (1, -4), (3, 8), (4, 5), (5, 4), (8, 3)
5 favorable / 10 possible
1/2
