Maybe you can first explain what exactly is meant by "board combinations?" My answer was long because I explained three different interpretations of "board combinations". 

I thought you might be referring to the number of possible positions in a game of chess that were achievable from the initial starting position via legal moves, but your question could also be referring to the number of combinations that 8 white pawns, 8 black pawns, 2 white rooks, 2 black rooks, 2 white knights, 2 black knights, 2 white bishops, 2 black bishops, 1 white queen, 1 black queen, 1 white king, and 1 black king (and subsets of these piece combinations) could be arranged on a 64-square grid, without any special regard for the rules of the game or legality of the position. Finally, you might be asking about the number of legal positions (for instance, Kings not being placed adjacently to one another) but not requiring that the position must be reachable from the initial position. 

Since the term combinations is a bit vague, I also explained how Shannon estimated the number of possible chess games. He knew that on average, Chess games last around 40 moves, and that for each pair of moves (a move by each player, or one full turn) has a "branching factor" of around 1000. To calculate the number of possibilities across the whole game, Shannon took 1000 to the power of 40. The result was around 10^120. However, this was based on a crude calculation and the exact number is not known.
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