The number of ways a deck of 52 cards can be distributed among 13 players such that each player receives 4 cards is given by the multinomial coefficient (52!/(4!)^13).

Here's the step by step calculation:

1. The total number of ways to arrange 52 cards is 52 factorial (52!).

2. For each player, the number of ways to arrange their 4 cards is 4 factorial (4!).

3. Since there are 13 players, we raise 4! to the 13th power.

4. The number of ways to distribute the cards is then 52! divided by (4!)^13.

This calculation assumes that the order in which the players receive the cards matters. If the order does not matter (i.e., all that matters is which 4 cards each player ends up with, not the order in which they received them), then the calculation would be different.

Question

The number of ways a deck of 52 cards can be distributed among 13 players such that each player receives 4 cards is given by the multinomial coefficient (52!/(4!)^13).

Here's the step by step calculation:

1. The total number of ways to arrange 52 cards is 52 factorial (52!).

2. For each player, the number of ways to arrange their 4 cards is 4 factorial (4!).

3. Since there are 13 players, we raise 4! to the 13th power.

4. The number of ways to distribute the cards is then 52! divided by (4!)^13.

This calculation assumes that the order in which the players receive the cards matters. If the order does not matter (i.e., all that matters is which 4 cards each player ends up with, not the order in which they received them), then the calculation would be different.

Knowee AI · Accepted Answer

The number of ways a deck of 52 cards can be distributed among 13 players such that each player receives 4 cards is given by the multinomial coefficient (52!/(4!)^13).

Here's the step by step calculation:

1. The total number of ways to arrange 52 cards is 52 factorial (52!).

2. For each player, the number of ways to arrange their 4 cards is 4 factorial (4!).

3. Since there are 13 players, we raise 4! to the 13th power.

4. The number of ways to distribute the cards is then 52! divided by (4!)^13.

This calculation assumes that the order in which the players receive the cards matters. If the order does not matter (i.e., all that matters is which 4 cards each player ends up with, not the order in which they received them), then the calculation would be different.

in how many ways can a deck of 52 cards be distributed among 13 players in such a way that each player can receives 4 cards?

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In how many ways can a deck of 52 cards be distributed among 13 players in such a way that each player can receives 4 cards?

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