Hello, nafiro!

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

There are: . 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: . ways.

. . To get 5 black cards, there are: . ways.

Hence, there are: . ways to get more than 3 black cards.

Therefore: .