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, has two cards per pile.     

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

 

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

   and that's when it's the stack consisting of both of the Two's.     

 

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

   _.