Problem Solving

We are just choosing two different integers from 1 to 10 inclusive, and want to know the probability they aren't consecutive. There are a few ways to do this, for example - we can choose 2 integers from 10 in 10C2 ways, so in 10*9/2 = 45 ways. That's our denominator. Now the only pairs of integers we don't want are the pairs of consecutive integers, so we want to rule out the selections {1, 2}, {2, 3}, {3, 4}, ... {9, 10}. So there are 9 selections we don't want, and thus 45-9 = 36 selections we do want, and the answer is 36/45 = 4/5.