# When to use which?

• August 11th 2007, 09:33 PM
wby
When to use which?
if 5 card are dealt from 52 cards, determine the probabilty of getting 3 red cards and 2 black face cards.

The answer is 26C3(6C2)/52C5, but I got 52C5(1/2)^5(6/52)^2, how do you know when to use which?

Thank you!
• August 12th 2007, 03:26 AM
Soroban
Hello, wby!

Quote:

If 5 cards are dealt from 52 cards,
determine the probabilty of getting 3 red cards and 2 black face cards.

The answer is: . $\frac{\left(_{26}C_3\right)\left(_6C_2\right)}{_{5 2}C_5}$

but I got: . $\left(_{52}C_5\right)\left(\frac{1}{2}\right)^5\le ft(\frac{6}{52}\right)^2$ . ??

How do you know when to use which?

Sorry, but everything you wrote is incorrect . . .

That $_{52}C_5$ is the number of possible 5-card hands.

. . It belongs in the denominator.

When they state "Five cards are dealt",

. . we generally assume it is without replacement.

So the probability of getting a certain color is not $\frac{1}{2}$ each time,
. . and the probability of getting a black face card is not $\frac{6}{52}$ each time.

. . There are: . $_{26}C_3$ ways.
. . There are: . $_6C_2$ ways.
. . Hence, there are: . $\left(_{26}C_3\right)\left(_6C_2\right)$ ways to draw 3 red cards and 2 black face cards.
And that is over $_{52}C_5$, the number of possible 5-card hands.