Q2 The Number of Matches In parts (a) - (d) below, assume that all participants are acceptable to each other. In other words, any man or woman prefer to be matched with somebody of the opposite gender rather than staying single. (a) Consider a marriage problem with two men and two women (i.e., a 2x2 market). Calculate the number of all possible matches where everyone is matched (i.e., nobody stays single). Also calculate the maximum possible number of stable matches (provide sample preferences which generate the maximum number of stable matches). (b) Consider a marriage problem with three men and three women (i.e., a 3x3 market). Cal- culate the number of all possible matches where everyone is matched (i.e., nobody stays single). (c) Consider a marriage problem with three men and three women (i.e., a 3x3 market). Suppose that one man and one woman rank each other as their first choice. Calculate the maximum possible number of stable matches. (d) Consider a marriage problem with four men and three women (i.e., a 4x3 market). Calculate the number of possible matches in which all women are matched with men