Creating 6 piles from 54 cards, what is the chance of 1 having 9 blacks and 1 having 9 reds?

Question

With a randomly shuffled $54$ card deck (including the $2$ jokers), I made $6$ piles of $9$ cards, placing $1$ card in each pile sequentially.

What are the chances $1$ pile is entirely black and another is entirely red?
This happened earlier

Answer 1

Since there are only 26 cards in a colour, you cannot have more than two hands with whole red, and likewise for black.

You seek the probability for:

• One whole red, one whole black, and four mixed hands.
• One whole red, two whole black, and three mixed hands.
• Two whole red, one whole black, and three mixed hands.
• Two whole red, two whole black, and two mixed hands.

Use the principle of inclusion and exclusion to count these hands.