Playing a game with 6 flat disks which have different colored sides (red and blue) calculate the probability of all the possible outcomes grouped together(ex: One grouping would be all the outcomes in which there are 4 blue and 2 red)

This is a binomial distribution, with P(red) = 0.5 and P(blue) = 0.5. There are 6 disks, so the probability of any one particular color arrangement is (0.5)^6. This, in turn, gets multiplied by the number of combinations of 6 things, taken r at a time, for each r from 0 through 6. For example, for 4 blue and 2 red, you'd multiply (0.5)^6 * C(6 , 2).