What is the probability that a five-card poker hand con- tains the 2 diamonds and 3 spades?
My Approach/Attempt-: N(contains 2 diamonds and 3 spades)=$\binom{4}{1} * \binom{13}{2} * \binom{4}{1} *\binom{13}{3}$
$\binom{4}{1}$ $\Rightarrow$ For selecting one suite which is diamond.
$\binom{13}{2}$ $\Rightarrow$ For selecting 2 cards from diamond.
$\binom{4}{1}$ $\Rightarrow$ For selecting one suite which is Spade.
$\binom{13}{3}$ $\Rightarrow$ For selecting 3 cards from spade.
$P\left ( E \right )=\left ( \binom{4}{1}*\binom{13}{2}*\binom{4}{1}*\binom{13}{3} \right )/\binom{52}{5}$ Am i correct?