# Math Help - How Many Possibilities?

1. ## How Many Possibilities?

Suppose five cards are drawn from a standard (52 card) deck of cards. From the 5 cards chosen, 3 are red and 2 are black. How many possibilities are there for this hand?

2. Originally Posted by magentarita
Suppose five cards are drawn from a standard (52 card) deck of cards. From the 5 cards chosen, 3 are red and 2 are black. How many possibilities are there for this hand?
There are twenty-six red and twenty-six black cards.
Choose three reds and two blacks.

3. ## do you...

Originally Posted by Plato
There are twenty-six red and twenty-six black cards.
Choose three reds and two blacks.
You mean 3/26 + 2/26 or 3/26 times 2/26?

4. ## Combinatorics question

Hello magentarita
Originally Posted by magentarita
You mean 3/26 + 2/26 or 3/26 times 2/26?
Neither. Plato means choose 3 from 26 and then 2 from 26. So the total number of choices is

$\binom{26}{3}\times\binom{26}{2} = 845000$

5. Originally Posted by magentarita
You mean 3/26 + 2/26 or 3/26 times 2/26?
Neither of those.
$\binom{26}{3}\cdot \binom{26}{2}$