I got upset one day that I couldn't quickly figure out the probability of meeting a number when summing the results of rolling an arbitrary set of dice. After a week of research (and four or five revisions over the proceeding weeks), I wrote the following program in J:
(}. %&(+/) ]) ($&0@# , +//.@(*/)/&: ($&1"0))
which tells me that the probability of rolling a 14 or better, given a set of (perfect) dice with number of sides 4 6 and 10, is 30.4167%.
And that is how I got interested in combinatorics.