Try this :
Remove the top-left corner and the bottom-right corner of a chessboard (thus remain 62 cases).
You have a set of double 9 dominoes. Pick up 31 of these dominoes. How many ways are there to fill in the chessboard with these 31 dominoes ? This only includes the position of the dominoes, not the way they're placed (that means if you have 1-9, it matters that it's in A-6 and A-7, but it doesn't matter whether the 1 is on A-6 or A-7).