It is easy enough for me to draw out the 36 possibilities of 2d6 to find these odds, but I would like to know what method can be used to calculate these odds for 2d6, 3d6, and 4d6. I have been banging my head against the wall with this problem for several days and I still fail to get a firm grasp of the proper concepts. I have not worked with probability calculations for many years and I would appreciate any guidance for this personal project of mine.

Below is a table that I would like to complete. For example, what is the probability of rolling at least 3 AND at least 5 using 2d6? Initially I had wanted to calculate odds with re-rolls added in, but I am having a hard enough time with just the flat rolls.

_______|2d6|3d6|4d6|

3+ & 3+ |___|___|___|

4+ & 3+ |___|___|___|

5+ & 3+ |___|___|___|

6+ & 3+ |___|___|___|

4+ & 4+ |___|___|___|

5+ & 4+ |___|___|___|

6+ & 4+ |___|___|___|

5+ & 5+ |___|___|___|

6+ & 5+ |___|___|___|

6+ & 6+ |___|___|___|

Thank you anyone who takes the time to help with my request.