Probability that every player gets 1 queen, jack, and king The four jacks, queens, and kings from a standard deck of cards are shuffled, and three cards are dealt to each of four players. Compute the probability that each player gets one jack, one queen, and one king.
I know that there are $12$ cards total and since every player gets one jack, one queen, and one king, would it be $\binom{12}3$ for the first player?

Taking the probabilities of each card dealt we get this product of fractions:
$$\frac{12}{12}\frac{8}{11}\frac{4}{10}\frac{9}{9}\frac{6}{8}\frac{3}{7}\frac{6}{6}\frac{4}{5}\frac{2}{4}\frac{3}{3}\frac{2}{2}\frac{1}{1}=\frac{72}{1925} \approx 0.03740$$
I notice that this can be expressed as: $$\frac{(3!)^4(4!)^3}{12!}$$
I can't explain why though.
