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The following cards are split into three piles at random, so that every pile contains the same number of cardsaThe 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.

Sagot :

kirigayuuki02
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%.
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