TITLE: Combinatorics bridge card game.
QUESTION [0 upvotes]: Bridge is played with four players and an ordinary deck of 52 cards. Each player begins with a hand of 13 cards. In how many ways can a bridge game start?
(Ignore the fact that bridge is played in partnership)
Here is my attempt: For the first player I have $52 \choose 13 $. For the second player I have $39\choose 13$. Then third player $26\choose 13$ and lastly $13\choose 13$.
Therefore, I have $52\choose 13$$39\choose 13$$26\choose 13$$13\choose 13$ of ways a bridge game can start.
Am I correct with this ? Is there another way to think this questions?

REPLY [0 votes]: I am attaching a link to another way of looking at the problem.
http://personal.psu.edu/drh20/250h/spring2002/practice/quiz07.pdf
Basically, what they are saying is that each card can belong to Player 1, 2, 3, or 4. So color all the cards of Player 1 red, Player 2 blue, Player 3 green and Player 4 yellow. Then ultimately you have 13 cards of each color type and you have to put them all in a deck and use permutation to get the number of ways. This gives us
$$\frac{52!}{13!13!13!13!}$$
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