Hello, wby!

Sorry, but everything you wrote is incorrect . . .If 5 cards are dealt from 52 cards,

determine the probabilty of getting 3 red cards and 2 black face cards.

The answer is: .

but I got: . .??

How do you know when to use which?

That is the number of possible 5-card hands.

. . It belongs in thedenominator.

When they state "Five cards are dealt",

. . we generally assume it iswithoutreplacement.

So the probability of getting a certain color isnoteach time,

. . and the probability of getting a black face card isnoteach time.

Their answer is correct.

You want to draw 3 red cards from the available 26 red cards.

. . There are: . ways.

You want to draw 2 black face cards from the available 6 black face cards.

. . There are: . ways.

. . Hence, there are: . ways to draw 3 red cards and 2 black face cards.

And that is over , the number of possible 5-card hands.