Editing State space (computer science) (section)

====Finite====
If the size of the state space is finite, calculating the size of the state space is a [[Enumerative combinatorics|combinatorial]] problem.<ref name=SACEA/> For example, in the [[eight queens puzzle]], the state space can be calculated by counting all possible ways to place 8 pieces on an 8x8 chessboard. This is the same as choosing 8 positions without replacement from a set of 64, or
:<math> \binom{64}{8} = 4,426,165,368</math>
This is significantly greater than the number of legal configurations of the queens, 92. In many games the effective state space is small compared to all reachable/legal states. This property is also observed in [[chess]], where the effective state space is the set of positions that can be reached by game-legal moves.  This is far smaller than the set of positions that can be achieved by placing combinations of the available chess pieces directly on the board.