How many isotopologues of water are there?
In an example as small as this, you could hypothetically construct all the cases, or at least enough of them to see that $9$ is incorrect. 

The only thing you need to change to get the right answer is instead of using $3\choose{2}$ which is a combination without replacement, you need to do combinations with replacement so ${2+3-1}\choose{2}$$=6$ ways to choose the hydrogens. We can very quickly verify this result by writing out the pairs of masses and seeing how many unique combinations we can make: 11 22 33 12 13 23. And then of course each of those combinations can have one of the three different types of oxygen, so 18 possibilities total. If you haven't seen combinations with replacement before, go here to learn more about them.