a) In chess, the king can move one position in any direction. Assuming that the king is

Question:

a) In chess, the king can move one position in any direction. Assuming that the king is moved only in a forward manner (one position up, to the right, or diagonally northeast), along how many different paths can a king be moved from the lower-left comer position to the upper-right corner position on the standard 8X8 chessboard?
b) For the paths in part (a), what is the probability that a path contains (i) exactly two diagonal moves? (ii) exactly two diagonal moves that are consecutive? (iii) an even number of diagonal moves?
Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Question Posted: