Find the probability of the following card hands-from a 52 card deck. In poker, aces are either high or low. A bridgehand is made up of 13 cards.
-A royal flush (5 highest cards of a single suit) in poker
A) $2.75 \times 10^{-4}$
B) $1.54 \times 10^{-6}$
C) $3.85 \times 10^{-7}$
D) $1.98 \times 10^{-3}$

Question

Quizplus · Accepted Answer

There are 4 suits and 10 different ranks (ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king). So, there are 4 * 10 = 40 different cards that are not aces. There are 4 * 4 = 16 different ways to choose the suit of the royal flush. There are 10 different ways to choose the highest card of the royal flush. There are 9 different ways to choose the next highest card of the royal flush. There are 8 different ways to choose the next highest card of the royal flush. There are 7 different ways to choose the next highest card of the royal flush. So, there are 16 * 10 * 9 * 8 * 7 = 80640 different royal flushes. The probability of getting a royal flush is 80640 / (52 choose 5) = 1.54 * 10^-6.

Find the Probability of the Following Card Hands-From a 52 2.75×10−42.75 \times 10^{-4}2.75×10−4

Find the Probability of the Following Card Hands-From a 52 $2.75 \times 10^{-4}$