SuIn buying a ticket in state-sponsored lottery, one selects a subset T consisting of 6 distinct numbers from set of the first 48 positive integers. After the sales are closed, a machine chooses at random 6 numbers out of these same 48; these 6 numbers constitute winning set, W. If T=W, the ticket holder wins jackpot. If T and W have 5 numbers in common, the ticket holder wins second prize. If T and W have 4 numbers in common, the ticket holder wins the third prize. Find:
a) number of different tickets that can be sold;
b) number of distinct second-prize tickets;
c) number of distinct third prize tickets.