To solve this problem, we need to first determine how many ways we can split the cards into three piles so that each pile contains an Ace.
There are a total of 6 cards, and we want to place the 4 Aces in the 3 piles. This is a combinatorial problem known as "Stars and Bars" or "Balls and Bins". We can calculate the number of ways to distribute the Aces using the formula:
C(4 + 3 - 1, 3 - 1) = C(6, 2) = 15
Now, let's calculate the total number of ways to split the 6 cards into 3 piles:
Total number of ways = 3^6 = 729
Therefore, the probability that every pile contains an Ace is:
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 15 / 729
Probability ≈ 0.02055
So, the probability that every pile contains an Ace is approximately 0.02055 or about 2.055%.
