We roll five standard dice (sides numbered 1 to 6) and write down the sum of the top three i.e. of the 3 highest values.
What is the probability to get 15 ?

(In reply to re(2): Perhaps.... ) A HINT by ed bottemiller)

(why is a program NOT "analytic" one still needs an unambiguous problem to be solved)

This is a good question and the answer is that it depends. For a problem like the present one I would regard a computer-based approach as the obvious one, hence my earlier observation commending Vishal's courage in trying his hand at an analytical solution. In some other cases, computer based approaches (in particular some of Charlie's) have proved fully as elegant as more analytic ones in the way in which they have produced solutions. On still other occasions simply brute-force testing a large field of possible solutions rather than approaching the problem head-on seems to me somewhat to miss the whole point of the exercise. Just a personal view - others may disagree, as is their right.

Posted by broll on 2010-11-16 14:10:44