A particle moves from (0,0) to (n,n) directed by a fair coin. For each head it moves one step east and for each tail it moves one step north. At (n,y),y<n, it stays there if a head comes up and at (x,n),x<n, it stays there if a tail comes up. Letk be a fixed positive integer. Find the probability that the particle needs exactly 2n+k tosses to reach (n,n). probabilitycombinatoricscountingIMO Shortlist