How many five-card hands dealt from a standard deck of $52$ playing cards are all of the same suit? If a random hand is dealt, what is the probability that it will have this property?
Would the probability be: $$\frac{\dbinom{13}{5}*\dbinom{4}{1}}{\dbinom{52}{5}}$$
Best Answer
It would be $$\frac{\binom41_{\text{color}} \cdot \binom{13}5_{\text{cards of this color}} \cdot \binom{52-13}0_{\text{other cards}}}{\binom{52}{5}_{\text{total}}} = \frac{\binom41 \cdot \binom{13}5}{\binom{52}5} = \frac{33}{16660}$$ So you are correct. See here for some more on the number.