You're overcounting by a factor of 6! = 720, because you're counting different orderings of the same numbers multiple times. "1,2,3,4,5,6" and "6,5,4,3,2,1" are not different tickets.
With 54 x 53 x 52 ... you get all of the permutations of all the sequences. It generates 1,2,3..., 2,1,3..., 3,1,2..., etc.
Yeah, I missed that. And each sequence has 6! permutations. Etc.