Question 51
In preparation for a game of Fish, Carl must deal 48 cards to 6 players. For each card that he deals, he runs through the entirety of the following process:
1. He gives a card to a random player.
2. A player $Z$ is randomly chosen from the set of players who have at least as many cards as every other player (i.e. $Z$ has the most cards or is tied for having the most cards).
3. A player $D$ is randomly chosen from the set of players other than $Z$ who have at most as many cards as every other player (i.e. $D$ has the fewest cards or is tied for having the fewest cards).
4. $Z$ gives one card to $D$.
He repeats steps 1-4 for each card dealt, including the last card. After all the cards have been dealt, what is the probability that each player has exactly 8 cards?
1. He gives a card to a random player.
2. A player $Z$ is randomly chosen from the set of players who have at least as many cards as every other player (i.e. $Z$ has the most cards or is tied for having the most cards).
3. A player $D$ is randomly chosen from the set of players other than $Z$ who have at most as many cards as every other player (i.e. $D$ has the fewest cards or is tied for having the fewest cards).
4. $Z$ gives one card to $D$.
He repeats steps 1-4 for each card dealt, including the last card. After all the cards have been dealt, what is the probability that each player has exactly 8 cards?