In an election, candidate A receives n votes and candidate B receives m votes, where n > m. Assume that in the count of the votes all possible orderings of the n+m votes are equally likely. Let Pn,m denote the probability that from the first vote on A is always in the lead. Find

(a) P2,1

(b) P3,1

(c) Pn,1

(d) P3,2

(e) P4,2

(f) Pn,2 (g) P4,3 (h) P5,3 (i) P5,4

(j) Make a conjecture as to the value of Pn,m.