PLEASE HELP WITH ARTIFICIAL INTELLIGENCE, THANK YOU IN ADVANCE. I'LL DEFINETELY UPVOTE IF YOUR SOLUTION IS CORRECT!!

1. (25 pt) Consider the game of Chess (https://en.wikipedia.org/wiki/Chess). Approximately how many different states can a chess game have? You may assume a. We do not consider pawn promotion b. We consider each pawn is a distinct piece c. We consider only states with no captured pieces, i.e all states will have 32 pieces d. We do not consider pawn promotion, castling, or any other special cases. State any other assumptions made and show your work. Your answer does not have to be mathematically correct, but should be in the right magnitude for the assumptions you have made and make sense based on your math. 2. (25pt) A farmer has just bought a wolf, a goat, and a cabbage. They must cross the river to get home, but their small rowboat can only carry the farmer and 1 animal or vegetable at a time. However, the farmer cannot leave the goat unsupervised with the cabbage, or the goat will eat the cabbage. Similarly, the farmer cannot leave the goat unsupervised with the wolf, or the wolf will eat the goat. Draw the full search space starting from the initial state below. Indicate with different colors or labels which states would not be further explored because something gets eaten, as well as which states would not be further explored because they are repeats of previous states (to avoid cycles)