# Thread: In a card game of euchre

1. ## In a card game of euchre

there are 24 cards and you get 5 cards what is the probability of having more than 3 black cards

2. Hello, nafiro!

I will assume that there are 12 black cards and 12 red cards.

There are 24 cards and you get 5 cards.
What is the probability of having more than 3 black cards
There are: . ${24\choose5} \,=\,42,\!504$ possible 5-card hands.

"More than 3 black cards" means "4 blacks cards or 5 black cards".

. . To get 4 black cards and 1 red, there are: . ${12\choose4}{12\choose1} \,=\,495\cdot12 \,=\,5940$ ways.
. . To get 5 black cards, there are: . ${12\choose5} \,=\,792$ ways.

Hence, there are: . $5940 + 792 \:=\:6732$ ways to get more than 3 black cards.

Therefore: . $P(\text{more than 3 black cards}) \;=\;\frac{6732}{42,\!504} \;=\;\frac{51}{322}$