I'm trying to analyse a game of Mastermind and am having trouble quantifying the amount of possible game states. I know that a code has $\text{# of colors}^{\text{# of pegs per guess}}$ combinations (in my case that would be $6^4=1296$). However, an entire board state also consists of 10 guesses. Each guess has the same amount of combinations, thus my intuition would be that the amount of total states in a game of Mastermind would be $\text{# of rows}^{\text{# of combinations per row}}$. This approach yields $11^ {1296}$ board states which is astronomically large and I'm having a hard time believing this is true.
To clarify what I mean by a board state, I mean any legal state the game board can be in using the standard game rules. Having 3 empty rows, then one guess row and another 6 empty rows is not a legal board state.
How do I go about estimating this number?