If a number between 10 and 50 (inclusive) at random.

You could also solve this problem with what's called a probability tree. It's basically the same idea as counting but with a handy tree visualization!

From the "top" of the tree, draw 5 branches going down, labelled 1,2,3,4 and 5 at the bottom of the "branch". These represent your choices for the first digit.

From each of the 1-4 branches, draw 10 more branches labelled 0-9. These represent your choices for the 2nd digit. From the 5 branch, draw one branch, labelled 0, as that's your only choice from that branch.

Now count the total branches at the "bottom". 10+10+10+10+1= 41. That's the denominator of your answer.

Now count the branches that meet your goal (ones digit greater than tens digit): 10, 20, 21, 30, 31, 32, 40, 41, 42, 43, 50. That's 11 numbers and that's your numerator.

Final answer: 11/41.

I use the tree whenever I get stuck on a probability question.