Counting

 

   The following cards are split into three piles at random, so that every pile contains     

   the same number of cards.  What is the probability that every pile contains an Ace?     

 

   Ace of spades     

   Ace of hearts     

   Ace of diamonds     

   Ace of clubs     

   Two of spades     

   Two of hearts     

 

   Six cards, divided evenly into three piles, each pile has two cards.     

   There can be ₆C₂ different piles, i.e., 15 different combinations.     

 

   There's only way that a pile won't contain at least one Ace,     

   and that is when the stack cosists of both of the Two's.     

 

   So, 14 will and 1 won't, makes the probability 14 / 15, i.e., 93.33%.     

   _.