2008 AIME I Problem 9

Ten identical crates each of dimensions 3 ft \times 4 ft \times 6 ft. 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 \frac {m}{n} be the probability that the stack of crates is exactly 41 ft tall, where m and n are relatively prime positive integers. Find m.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.