Find the probability of the following five-card poker hands from a 52-card deck. In poker, aces are either high or low.
-Royal flush (5 highest cards of a single suit)
A) $\frac { 1 } { 2598960 }$
B) $\frac { 2 } { 162435 }$
C) $\frac { 1 } { 649740 }$
D) $\frac { 1 } { 64974 }$

Question

Quizplus · Accepted Answer

A royal flush consists of the 10, J, Q, K, and A of the same suit. There are 4 suits, so there are 4 possible royal flushes. The total number of 5-card combinations from a 52-card deck is $\binom{52}{5} = 2,598,960$. Thus, the probability is $\frac{4}{2,598,960} = \frac{1}{649740}$.

Find the Probability of the Following Five-Card Poker Hands from a 52-Card