What is the probability of getting STRAIGHT FLUSH in a $13$-card poker game?
Here is my attempt:
A straight flush is five cards in sequence and of the same suit, but not ace king queen jack ten.
The required probability is $$\dfrac{9 \cdot {4 \choose 1}}{{52 \choose 13}} = \dfrac{36}{635013559600} = \dfrac{9}{158753389900} \approx 5.66917028081678777\ldots \cdot{10}^{-11}.$$
My questions are:
(1) Is this probability computation correct?
(2) If my computation is not correct, where is/are the error(s) and what hint can you give towards rectifying that error(s)?
Your are missing the extra cards
It is 52 - 6 as you cannot have the card above of it makes a higher straight
This is for one
$$\frac {\binom{9}{1} \binom{4}{1} \binom{46}{8} } { \binom{52}{13} } = 0.01479 \approx 1 / 67.6$$
I think this is 2
$$\frac {\binom{9}{1} \binom{4}{2} \binom{40}{3} } { \binom{52}{13} } = 0.00000084 \approx 1 / 1190234$$