# Help with question on a deck of cards please

• May 3rd 2010, 09:37 AM
roushrsh
Help with question on a deck of cards please
Ok, well the question in my book says that there are 52 cards in a deck of cards. How many possibilities are there if we are to take 6 cards randomly out of the deck if 2 of them have to be face cards (king, queen, jack).
Can someone please explain to me how to do this with the answer so I can verify? thank you

I thought something like 40!/4! but that seems totally wrong -.-
• May 3rd 2010, 10:07 AM
Soroban
Hello, roushrsh!

Quote:

There are 52 cards in a deck of cards.
How many possibilities are there if we are to take 6 cards randomly out of the deck
if two of them have to be face cards (King, Queen, or Jack)?

There are: . $\begin{Bmatrix}\text{12 Face cards} \\ \text{40 Others} \end{Bmatrix}$

We want two Face cards: . ${12\choose2}$ ways.

And we want four Others: . ${40\choose4}$ ways.

If the question means exactly two Face cards, the answer is:

. . $\frac{12\!}{2!\,10!}\cdot\frac{40!}{4!\,36!} \;=\;66 \times 91,\!390 \;=\;6,\!031,\!740$ possibilities.

• May 4th 2010, 09:07 AM
roushrsh
thank you very much :)