Big 2 is a card game commonly played in Asia.

Big Two - Wikipedia, the free encyclopedia

There are 4 playeers and each is dealt 13 cards. The trump cards in this game is 2, hence the name Big 2. My question is:

What's the probability of 1 player dealt 4 '2's?

Method 1:

$\displaystyle {{48 \choose 9} \over {52 \choose 13}} = {11 \over 4165}$

Method 2:

Using the ball-and urn model championed by William Feller,

we imagine 4 people as 4 urns, and the 4 '2's to be dealt as 4 balls:

So now, we are asking what's the probability of all 4 balls landing inside 1 urn:

The probability of 4 balls inside 1 urn(and not 3 others): $\displaystyle ({1 \over 4})^4 = {1 \over 256}$

Since it can be any of the 4 urns, we multiply by 4 and get $\displaystyle {4 \over 256}$

Now, why don't the 2 methods tally?

Can anyone please explain?

Much appreciated!