3 dice probability question

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?

I'm not sure I understand the problem. The experiment consists of tossing three dice. NOW, the rv X is the sum of the smaller two numbers of the three?

Yeah, the sum of the two smaller numbers. So I want to say what is the probability of rolling 8 or less on 3 dice where the highest number isn't counted.

It is tricky because the 'highest number' is going to be a variable, so anything from 1 to 6 could be removed depending on what all the dice say.

Roll 3 dice: 3 5 6. 6 is the highest, so remove. Total is 8. Roll again: 2 4 4. 4 is the highest so remove a 4, total is 6.