How To Set Up A Card Probability Problem Rosa draws a five-card hand from a $52-$card deck.  For each scenario, calculate the total possible outcomes:

Rosa’s hand has three red cards and three face cards.

The only way I could think about doing this was to add together the $26$ red cards, along with the face cards, since half of them are already red, it was only $6$, which would give me $32$ cards that I am trying to get. At first I thought I would set this up like other problems I have done where I put $32/5$, but the answer is not right. 
Could someone please show me how to set this up?

Since Rosa's hand has $5$ cards and the conditions are $3$ red and $3$ face cards, at least one card has to be a "red, face card". Following hands satisfy the given conditions (please check that I did not forget something):


*

*$1$ red face card, $2$ red not-face cards, $2$ black face cards.

*$2$ red face cards, $1$ red not-face card, $1$ black face card, $1$ black not-face card.

*$3$ red face cards, $2$ black not-face cards.


Now, there are $6$ red face cards ($2$ J's plus $2$ Q's plus $2$ K's), $20$ red not-face cards and the same for black. So,


*

*Possible ways: $$\dbinom{6}{1}\cdot\dbinom{20}{2}\cdot\dbinom{6}{2}=17100$$

*Possible ways: $$\dbinom{6}{2}\cdot\dbinom{20}{1}\cdot\dbinom{6}{1}\cdot\dbinom{20}{1}=36000$$

*Possible ways: $$\dbinom{6}{3}\cdot\dbinom{20}{2}=3800$$
Hence the total ways are equal to $$17100+36000+3800=56900$$

