In the game of euchre, the deck consists of the 9, 10, jack, queen, king and ace of each suit. Players are dealt a five card hand.
What is the probability that a player is dealt 3 kings? =
To find the probability of being dealt 3 kings in a game of euchre, we need to determine the total number of possible hands and the number of favorable outcomes.
Step 1: Determine the total number of possible hands.
In euchre, players are dealt a 5-card hand from a deck of 24 cards (excluding 6s, 7s, and 8s). Therefore, the total number of possible hands can be calculated using combinations. The formula for combinations is nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items chosen.
In this case, we have 24 cards in the deck and want to choose a 5-card hand. Using the combination formula, we can calculate the total number of possible hands as follows:
Total number of possible hands = 24C5 = 24! / (5!(24-5)!) = 42,504
Step 2: Determine the number of favorable outcomes.
To have 3 kings in the hand, we need to choose 3 kings out of the total 4. Similarly, we need to choose 2 cards out of the remaining 20 non-king cards. Using the combination formula, we can calculate the number of favorable outcomes as follows:
Number of favorable outcomes = (4C3) * (20C2) = 4! / (3!(4-3)!) * 20! / (2!(20-2)!) = 4 * 190 = 760
Step 3: Calculate the probability.
The probability of being dealt 3 kings can be calculated by dividing the number of favorable outcomes by the total number of possible hands.
Probability = Number of favorable outcomes / Total number of possible hands
= 760 / 42,504
≈ 0.0179
Therefore, the probability of being dealt 3 kings in a game of euchre is approximately 0.0179, or 1.79%.