In a certain game, a one-inch square piece is placed in the lower left corner of an eight-by-eight grid made up of one-inch squares. If the piece can move one grid up or to the right, what is the probability that the center of the piece will be exactly 4sqrt(2) inches away from where it started after 8 moves?
OK so i know the total out comes are 2^8...i can either go up or left..
there are 8 upward tracks..and 8 side tracks.. we are asked how can the tile be at the dead center..that means it will have to travel 4 ups..and 4 lefts..
ok so if the tile is on the corner..it has 7C4 ways to go up and 7C4 ways to go left..i.e total ways =70..
70/256 is my guess