Prove that there exists a positive integer N such that there are at least 2005 ordered pairs (x, y), of non-negative integers x and y, satisfying x^2 + y^2 = N.

Due to a packaging error, 4 cans labeled diet soda were accidentally filled with regular soda and placed in a 12 pack carton of diet soda. two cans were randomly selected from this 12 pack. what is the probability that both cans were regular soda?