Quote: if you got 8 decks of cards, you take 5 cards. waht is the possibility of atleast one ace of spades?
I assume you pick 5 cards w/o replacing them
at first pick odds of not picking an ace of spades is
51/52
2nd pick the chances are (8*51 - 1) / (8*52 - 1), i.e. # of non ace of spade cards left / # cards left
3rd pick the chances are (8*51 - 2)/ (8*52 - 2)
etc. up to 5
you get
{51/52, 407/415, 203/207, 405/413, 101/103}
multiply all these together to get your final probability for picking 5 non ace of spade cards
p = 547175277 / 603251636 ~ 0.91
now the probability of picking at least 1 ace of spades is (1 - p) ~ 0.09
+6251 
