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 will create two cards per pile.     

   This makes 6C2 possible different piles, i.e., 15 possible combinations.     
 

   AS AH      AH AD      AD AC      AC 2S      2S 2H     

   AS AD      AH AC      AD 2S      AC 2H     

   AS AC      AH 2S      AD 2H     

   AS 2S      AH 2H     

   AS 2H     

 

   As illustrated above, every combination will have an Ace, except one.     

   The only pile that doesn't contain an Ace is the pile that has both 2's.     

   So the probability that a pile will contain an Ace is 14 / 15, i.e., 93.3%.     

   _.