Let the number of games won and those lost by the man be Nw and N, respectively. Since he gains $2, Nw−Ni=2 . Also, he does not lose more than once. The possible cases are (W → Win and L → Loss): Case (i): Nw=2 and N1=0. The only possible sequence is WW. Case (ii):Nw=3 and N1=1. Possible sequences: LWWW and WLWW. Hence, the to tal number of possible Win-Loss sequences = 1 + 2 = 3.