What is the probability of a royal flush? How is it calculated?

Ritu13

The probability of getting a royal flush is indeed approximately 1 in 14,000. To calculate it:

1. First, you correctly identified that there are 9 possible royal flush combinations (from 10 to Ace) within each suit (hearts, diamonds, clubs, and spades).
2. Then, there are 4 suits in a standard deck.

So, you have:

Number of ways to get a royal flush = 9 (combinations) * 4 (suits) = 36

Now, to calculate the probability:

Probability = (Number of ways to get a royal flush) / (Total number of possible 5-card hands from a deck of 52 cards)

Total number of possible 5-card hands = C(52,5) = 2,598,960

So, the probability is:

Probability = 36 / 2,598,960 ≈ 1.38 x 10^(-5), which is indeed approximately 1 in 14,000

Niti998

"Anyway, I haven't encountered a royal flush in all these years."

Jatin255

"A one in 14,000 chance, that's very, very slim odds."

Kahn332

"People who haven't studied this wouldn't understand it either."