5. Consider a matching model where agents in X = {x1, x2, x3}, Y = {y1, 92, 93}, and Z = {21, 22, 23} are to be matched in triples (xi, yj, zk). Assume that all agents have strict preferences over pairs of agents from the other groups. A ranking function r: X x Y x Z {1,..., 9} rep- resents the preferences in the following way. r(x1,y2, 22)=(x1 (92, 22), Ty2 (1, 2), Tz2 (1, y2) = (2, 3, 6), means that x1 ranks (y2.22) as her second best option, y2 ranks (x1, Z2) as her third best option and z2 ranks (1, 92) as her sixth best option (and similarly for all possible triples). (a) How many different matchings are there?