# Probability of five card stud flush

I'm not really good dealing with poker problems...

I am doing a practice problem for a midterm coming up, and help would be appreciated.

Consider the probability that, in a game of five-card stud, you will be dealt a flush (i.e., five cards of the same suit).

By showing that the number of ways in which you may be dealt a flush is $(52 * 12 * 11 * 10 * 9)/5! = 4*13!/5!8! ~~5*10^3$, demonstrate that your chance of being dealt a flush is of the order of $\frac{1}{500}$.

• You could divide that number (actually $5148$) by the total number of equally probable hands ($2598960$) Feb 6, 2015 at 7:27
• That's what I was attempting on doing, so i got around the 1/520 range, is that an acceptable answer to the "order of 1/500"...sorry I'm terrible with the wording of these problems. Feb 6, 2015 at 7:31
• $\dfrac{5148}{2598960} \approx \dfrac{1}{505}$ while $\dfrac{5000}{2598960} \approx \dfrac{1}{520}$ so it is better to round at the end of a calculation rather than in the middle. Feb 6, 2015 at 7:35

You could divide that number (actually $5148$) by the total number of equally probable hands ($2598960$) to get $\dfrac{5148}{2598960} \approx \dfrac{1}{505}$.
It is better to round at the end of a calculation rather than in the middle, because if you use the hint's $5\times10^3$ you get $\dfrac{5000}{2598960} \approx \dfrac{1}{520}$.