Ten identical crates each have dimensions 3ft X 4ft X 6ft. The first crate is placed flat on the floor. Each of the remaining nine crates is placed, in turn, flat on top of the previous crate, and the orientation of each crate is chosen at random. Let m/n be the probability that the stack of the crates is exactly 41ft tall, where m and n are relatively prime positive integers.
I think I will have a total of 3x3x3x3x3x3x3x3x3x3 choices.
but for the height to be 41ft I don't think I can write them all out.
Could I please get some hints.
And what does relatively prime positive integers mean?