I’m designing a tabletop game, and I need to figure out how to calculate a few probabilities:
 Roll 3 20sided dice, take the highest value. What is the probability of it being 7 or higher? 15 or higher?

 Roll 4 20sided dice, take the highest value. What is the probability of it being 7 or higher? 15 or higher?

 Roll 3 20sided dice, take the lowest value. What is the probability of it being 7 or higher? 15 or higher?

 Roll 4 20sided dice, take the lowest value. What is the probability of it being 7 or higher? 15 or higher?
How can I do this? Could you explain to me how this works, or even better – give me a simple formula?