in how many way can a pack of 52 cards be divided equally among four players in order ?

Options

A. a. `(52 !)^4`
B. b. `4 xx (13!)`
C. c. `(52)/((13!)^4)`
D. d. none of these

Answer

To solve the problem of how many ways a pack of 52 cards can be divided equally among four players in order, we can follow these steps:

### Step 1: Determine the number of cards each player receives
Since there are 52 cards and they need to be divided equally among 4 players, we first calculate how many cards each player will get:
\[ \text{Cards per player} = \frac{52}{4} = 13 \]
Each player will receive 13 cards.

### Step 2: Calculate the total arrangements of the cards
Next, we need to find the total number of ways to arrange 52 cards. The number of arrangements of 52 cards is given by \(52!\) (52 factorial).

### Step 3: Divide the arrangements among the players
Since each player receives 13 cards, we need to account for the arrangements within each player's hand. The number of ways to arrange the 13 cards for each player is \(13!\). Since there are 4 players, we will have \( (13!)^4 \) to account for the arrangements of cards within each player's hand.

### Step 4: Calculate the total number of ways to distribute the cards
The total number of ways to distribute the cards can be calculated using the formula:
\[ \text{Total ways} = \frac{52!}{(13!)^4} \]
This formula accounts for the total arrangements of the cards divided by the arrangements within each player's hand.

### Conclusion
Thus, the total number of ways to divide a pack of 52 cards equally among 4 players in order is:
\[ \text{Total ways} = \frac{52!}{(13!)^4} \]