Final answer:
The total number of different hands possible when a player is dealt 6 cards from a standard 52-card deck in the game "Kings and Threes" can be calculated using combinations, resulting in 20,358,520 different hands.
Step-by-step explanation:
The question asks about the number of different hands possible in the card game "Kings and Threes" when a player is dealt 6 cards from a standard 52-card deck. To find this, we use the concept of combinations in probability. The total number of different hands can be calculated as a combination of 52 cards taken 6 at a time, which is denoted as 52C6.
Using the formula for combinations, which is nCk = n! / (k!(n-k)!), where n is the total number of items, and k is the number of items to be chosen, we can calculate 52C6 as:
52C6 = 52! / (6!(52-6)!) = 52! / (6!46!) = (52 x 51 x 50 x 49 x 48 x 47) / (6 x 5 x 4 x 3 x 2 x 1)
After cancelling out the common factors, we find that the total number of different hands possible is 20,358,520.