Hi folks,

in probability questions that ask the probability of getting say, 3 queens in a hand of 5 cards, the probability P is the ratio of the favourable outcomes to the total number of possible outcomes/hands. In a normal 52 card deck the total number of 5 card hands is the number of possible selections i.e. $^{52}C_{5} = 52!/47! \times 5!$ or 2,598,960. If the hands are of only 2 cards then the number of such hands is $^{52}C_{2}$ or 1326.

I have a question in which two cards are drawn (without replacement) from a deck of 52 and we are asked to find the probability that the first card is a spade and the second card is the king of spades.

As you see, it is slightly puzzling because of the order: What happens if I pull the king of spades with the first card? I decided to ignore this possibility. So the first card must be one of the other 12 spades, so there are 12 ways of selecting the first card and only one way of selecting the king of spades so favourable outcomes = 12 and the total Probability should be 12/1326 = 2/221 and this is wrong.

Of course, one could say that there are 12/52 ways of selecting the first card and 1/51 ways of selecting the second card which is 12/51.52 = 1/221 and get the right answer, but my question is what is wrong with the first method?