The mass of Earth is given in Physics (4th Edition, Volume I) by Resnick, Halliday, and Krane as 5.88x1024 kilograms. The mass of a neutron is 1.67x10-27 kilograms. This gives the number of neutrons in the earth to be about 3.52x1051, a gross overestimation of the number of atoms in the Earth. Even so, this number pales in comparison to 52!, which is about 8.07x1067, and even this number is merely the square root of the 52!x52! number of entries required in the transition matrix for a deck of cards.