help probability

 

   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 possible combinations.     

 

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

   and that's if the stack happens to be composed of both Two's.     

   Since there are 15 combinations, the chance of that is 1 / 15.     

 

   So, mathematically the other 14 times there will not be a pile     

   that has both Two's.  In other words, 14 times out of 15 every     

   pile will have at least one Ace.  Probability 14 / 15 = 93.33%     

   _.