what is the probability of getting a royal flush in poker?
I realize it is 4/C(52,5), but what are the combinations for the numerator?
Don't assume everybody knows what a royal flush is, I had to look it up
http://en.wikipedia.org/wiki/Hand_rankings#Straight_flush
There are 4 possible royal flushes.
the number of ways to choose any 5 cards
= C(52,5)
so the prob of a royal flush = 4/C(52,5)
= 4/2598960
= 1/649740
that sounds sooooooooooooooooooo hard .
i'm glad i don't have 2 do that !!
lv u xxxxxxx
To calculate the probability of getting a royal flush in poker, we need to determine the number of combinations for the numerator of the probability fraction. The numerator represents the number of successful outcomes (i.e., the number of ways to get a royal flush), while the denominator represents the total number of possible outcomes (i.e., the number of ways to select any 5 cards from a standard deck of 52 cards).
A royal flush consists of the following 5 cards: Ace, King, Queen, Jack, and Ten, all of the same suit (e.g., hearts, diamonds, clubs, or spades). Since there are 4 suits in a standard deck, we can calculate the number of combinations for the numerator as follows:
1. Choose the suit: There are 4 ways to choose the suit for a royal flush.
2. Choose the Ace: Once the suit is chosen, there is only 1 way to choose the Ace of that suit.
3. Choose the King, Queen, Jack, and Ten: For each suit, there is only 1 way to choose each of these remaining cards. Therefore, we have 1 choice for the King, 1 choice for the Queen, 1 choice for the Jack, and 1 choice for the Ten.
To find the total number of combinations for the numerator, we multiply these choices together:
Number of combinations for numerator = 4 (suit choices) * 1 (Ace choice) * 1 (King choice) * 1 (Queen choice) * 1 (Jack choice) * 1 (Ten choice) = 4
Therefore, the numerator of the probability fraction is 4.
Now, using combinatorial notation (C), we can calculate the denominator of the probability fraction as C(52, 5), which represents the number of ways to choose any 5 cards from a standard deck of 52 cards.
Now that we know the numerator and the denominator, we can calculate the probability of getting a royal flush in poker by dividing the number of successful outcomes (numerator) by the total number of possible outcomes (denominator):
Probability of getting a royal flush = 4 / C(52, 5)