Question 1058141: How do I determine the probability of drawing at least 3 face cards from a deck upon drawing 8 cards?
That is of the 8 cards drawn at least 3 are face cards.
Answer by solve_for_x(190)   (Show Source):
You can put this solution on YOUR website! The shorter way of doing this is to determine the number of ways that you could draw 0, 1, or 2
face cards in the 8 cards, and then subtract those values from the number of ways that you could
select ANY 8 cards from the deck.
Number of 8 card hands: C(52, 8) = 752,538,150
Number of ways to select 0 face cards (and 8 non-face cards): C(12, 0)*C(40, 8) = 1 * 76,904,685 = 76,904,685
Number of ways to select 1 face card (and 7 non-face cards): C(12, 1)*C(40, 7) = 12 * 18,643,560 = 223,722,720
Number of ways to select 2 face cards (and 6 non-face cards): C(12, 2)*C(40, 6) = 66 * 3,838,380 = 253,333,080
Total number of ways to select 0, 1, or 2 face cards = 76,904,685 + 223,722,720 + 253,333,080 = 553,960,485
Number of ways to select at least 3 face cards = 752,538,150 - 553,960,485 = 198,577,665
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