there are 24 cards and you get 5 cards what is the probability of having more than 3 black cards
Hello, nafiro!
I will assume that there are 12 black cards and 12 red cards.
There are: .$\displaystyle {24\choose5} \,=\,42,\!504$ possible 5-card hands.There are 24 cards and you get 5 cards.
What is the probability of having more than 3 black cards
"More than 3 black cards" means "4 blacks cards or 5 black cards".
. . To get 4 black cards and 1 red, there are: .$\displaystyle {12\choose4}{12\choose1} \,=\,495\cdot12 \,=\,5940$ ways.
. . To get 5 black cards, there are: .$\displaystyle {12\choose5} \,=\,792$ ways.
Hence, there are: .$\displaystyle 5940 + 792 \:=\:6732$ ways to get more than 3 black cards.
Therefore: .$\displaystyle P(\text{more than 3 black cards}) \;=\;\frac{6732}{42,\!504} \;=\;\frac{51}{322} $