Question

Find the probability of the following five-card poker hands from a 52-card deck. In poker, aces are either high or low. Two pair (2 cards of one value, 2 of another value)

Answer 1

a lot of counting for this one

Answer 2

there are \(\dbinom{52}{5}\) possible 5 card hands. that is the denoyminator

Answer 3

there are 13 different face values for each suit, so there are \(\binom{13}{2}\) ways to pick the two different face values

Answer 4

you have to take one pair from two suits, and another pair from two suits and there are \(\dbinom{4}{2}\times \dbinom{4}{2}\) ways to do this

Answer 5

now for the fifth card, you have 4 suits to choose from, and 11 different face values to choose from, so there are 44 ways to do this

Answer 6

final answer is
\[\frac{44\binom{13}{2}\binom{4}{2}\binom{4}{2}}{\binom{52}{5}}\]

Answer 7

oo thank you a bunch