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find the probability of getting a royal flush

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Understanding integers

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Q. find the probability of getting a royal flush

Count Total $5$ -Card Hands: Count the total number of possible $5$ -card hands from a standard $52$ -card deck. $\newline$ Calculation: There are $52$ cards, and we need to choose $5$ , so we use the combination formula which is $52C5$ . $\newline$ $52C5 = \frac{52!}{(5! * (52 - 5)!)}$ $\newline$ $52C5 = \frac{52!}{(5! * 47!)}$ $\newline$ $52C5 = 2,598,960$
Identify Royal Flush Ways: Identify the number of ways to get a royal flush. $\newline$ Calculation: A royal flush is a $10$ , $J$ , $Q$ , $K$ , $A$ all of the same suit. There are $4$ suits, so there are $4$ possible royal flushes.
Calculate Probability: Calculate the probability of getting a royal flush. $\newline$ Calculation: Probability = $\frac{\text{Number of royal flushes}}{\text{Total number of 5-card hands}}$ $\newline$ Probability = $\frac{4}{2,598,960}$ $\newline$ Probability = $\frac{1}{649,740}$

More problems from Understanding integers

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g(x)=-\frac{4}{3}|x|

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\$ 200

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