$52$ cards are dealt among 4 players, determine the probability that a player gets all the spades
Number of ways the cards can be dealt among $4$ players = $52 \choose {13,13,13,13} $$= \frac{52!}{(13!)^4}$
Number of ways player $1$ gets all the spades =$ 13\choose 13$$ 39\choose {13,13,13}$ = $\frac{39!}{(13!)^3}$
So the required probability should be = $$\frac{4*\frac{39!}{(13!)^3}}{\frac{52!}{(13!)^4}}$$
Is this correct? If not, please tell where is the mistake so that I can learn