A standard deck of 52 cards contains four suits: hearts, diamonds, clubs, and spades. Each suit has 13 cards: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king. Three cards are randomly drawn without replacement. Calculate the probability of drawing three heart cards.
To calculate the probability of drawing three heart cards, we first need to determine the total number of ways to draw 3 cards out of the 13 heart cards, which is given by the combination formula:
C(13, 3) = 13! / (3!(13-3)!) = 286
Next, we need to determine the total number of ways to draw 3 cards out of the 52 cards in the deck:
C(52, 3) = 52! / (3!(52-3)!) = 22,100
Therefore, the probability of drawing three heart cards is:
286 / 22,100 ≈ 0.01294 or approximately 1.29%