The Math Olympics?

ok so im in this math competition and im stuck on a practise question. here it is...


a china collector has 53 blue plates, 13 red plates, 76 green plates, and 9 yellow plates. each plate is wrapped in newspaper. how many plates will the collector have to unwrap to be sure of seeing 2 of each colour?





a) 5 plates b) 10 plates c) 12 plates d) 15 plates e) 18 plates





if you can figure it out will you please show me how you got it?





THANKS!!!!!!

The Math Olympics?
5 plates





You have 4 kind of plates with various quantities. If you opened 4, you have a chance of either opening two of a kind (already a match) or one of each. (no match) The worst case senario here is one of each. (no match)





Opening one more gurantees the last one is a duplicate of one already opened. Because you already have one of each. Whatever the last one you open, you already have one of each, thus a match.
Reply:But the question asks how many to see 2 of EACH COLOR. He could open all the blue red and green plates before opening any yellow. He would have to open those plus 2. 53+13+76+2 which is 144. That's the max number of plates youd have to open to be sure of opening 2 of each Report It