33 balls mumbered 1-33 in a bingo type dispenser let two balls out to attain #1 then #2 return the balls and repeat this operation until #1 then #2 are attained repeat the operation until this happens a second time How many tries are needed to achieve this?
I assume you are talking about drawing the balls numbered 1 and 2 without any respect to the order in which they are drawn. There are 33 ways to draw a ball out on the first draw and 32 ways to draw a second ball (assuming no replacement). Drawing a 1 and 2 is the same as drawing a 2 and 1 so that the number of cases are doubled, so just divide by 2. Now to the second part of your question, it appears that you are asking how many draws will take place before it happens again. It would seem to me that there is no way to determine this. I would welcome input from anyone else in this matter.