ron@brl-sem.ARPA (Ron Natalie <ron>) (11/28/85)
(* INCORRECT AND SPOILED *) > Soln: > a. First, the number of tickets that have no match: > 30*29*28*27*26*25 = 427518000 (na) > > b. The number of tickets that have EXACTLY one match: > (30*29*28*27*26) * (6*6) = 615625920 (nb) > . > . . number of tickets you may have to buy before you are sure > of getting at least two correct numbers: > na + nb + 1 = 1043143921 > ASSUMPTION 3: You can pick the numbers on the tickets yourself. You are not drawing tickets out of a pool of all possible tickets until you get one that works. And the key phrase that is wrong in your answer is not "MAY HAVE TO BUY" but is "WILL HAVE TO BUY." For instance, let's make the problem easier (this is akin to the Rubiks cube that only has one rotational axis): I have mini-LOTTO where I draw a number between one and ten. You buy tickets that you designate three numbers. What is the minimum number of tickets you need to be assured of matching my number. There are 10*9*8 possible tickets. Of this number 9*8*7 will be losers. However, you only need to buy four tickets 1,2,3 4,5,6 7,8,9 10,xx,xx The xx numbers don't matter.