I am trying to work out some probabilities involving 3 dice. Basically the probability of rolling equal to or lower than a certain number. Now I know that is easy enough, but there is a catch. The dice that rolls the highest must be discarded. For example, if the roll is 2, 3, 6 then the 6 is discarded and only the 2 and 3 are summed.

So an example question would be what are all results where 7 or less is rolled, discarding the highest. I know there are 216 possibilities (6*6*6) and I have drawn up a big excel spreadsheet using IF functions and such which I believe has given me the correct answers, but it is bugging me because I am sure there is an easier way to do it using equations and such. Any ideas?