SuIn buying a ticket in a statesponsored lottery one chooses

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

(a) the number of different tickets that can be sold;
(b) the number of distinct second-prize tickets;
(c) the number of distinct third prize tickets.

Solution

a) No of different tickets that can be sold = 48P6 = 8835488640

b) No of different second prize tickets = 6P5(48) = 288 tickets

c) No of iii price tickets = 6P4(48P2) = 67680 tickets.