A regular deck of 52 playing cards has 13 ranks in 4 suits. The ranks of Jack, Queen, King and Ace of each suit are top cards. Suppose you are randomly dealt seven cards. What is the probability of getting three top cards in the same suit and any four cards in another suit (but all four in one suit)?
This is what I was thinking of calculating but am completely unsure:
$$ { \begin{pmatrix} 4 \\ 3 \\ \end{pmatrix} × \begin{pmatrix} 39 \\ 4 \\ \end{pmatrix} × \begin{pmatrix} 9 \\ 4 \\ \end{pmatrix} \over \begin{pmatrix} 52 \\ 7 \\ \end{pmatrix} } = 0.30986...$$
Any help appreciated. Thanks.