Twelve tickets numbered 1 to 12 are put in a box and two of them are drawn together at random. What is the probability that both numbers drawn are even?

Two tickets out of twelve can be drawn in C(12,2) = 66 ways, and two of the six even tickets in C(6,2) = 15 ways, so the probability is 15/66 = 5/22. Drawing one at a time agrees: (6/12) × (5/11) = 5/22. Holding the second denominator at 12, as if the first ticket went back, gives (6/12)(6/12) = 1/4; dropping the numerator but not the denominator gives (6/12)(5/12) = 5/24; and 1/2 is only the chance that a single ticket is even.