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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.

 Dec 23, 2021
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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

 Dec 23, 2021

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