# How Many Possibilities?

• May 1st 2009, 01:01 PM
magentarita
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?
• May 1st 2009, 01:26 PM
Plato
Quote:

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.
• May 2nd 2009, 02:57 AM
magentarita
do you...
Quote:

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?
• May 2nd 2009, 03:24 AM
Combinatorics question
Hello magentarita
Quote:

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

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

$\displaystyle \binom{26}{3}\cdot \binom{26}{2}$