The number of ways to distribute m `xx` n different thing among n persons equally = `((mn)!)/((m!)^(n))`
The number of ways in which a pack of 52 card can be distributed among 4 players in a game bridge is

Options

A. `(52!)/(4!13!)`
B. `(52!)/(4xx13!)`
C. `(52!)/((13!)^(4))`
D. `(50xx4!)/(13!)`

Answer

To solve the problem of distributing a pack of 52 cards among 4 players in a game of bridge, we can use the formula for distributing \( m \times n \) things among \( n \) persons equally, which is given by:

\[ \frac{(mn)!}{(m!)^n} \]

### Step-by-Step Solution:

1. **Identify the values of \( m \) and \( n \)**:
- In this case, we have 52 cards to distribute among 4 players.
- Each player will receive an equal number of cards, which is \( m = 13 \) (since \( 52 \div 4 = 13 \)).
- The number of players is \( n = 4 \).

2. **Substitute the values into the formula**:
- We need to calculate the total number of ways to distribute the cards using the formula:
\[ \frac{(mn)!}{(m!)^n} \]
- Here, \( mn = 52 \) (total cards) and \( m = 13 \), \( n = 4 \).

3. **Calculate \( (mn)! \)**:
- We find \( (52)! \) since \( mn = 52 \).

4. **Calculate \( (m!)^n \)**:
- We need to calculate \( (13!)^4 \) because \( m = 13 \) and \( n = 4 \).

5. **Combine the results**:
- Now we can substitute these values back into the formula:
\[ \text{Total ways} = \frac{52!}{(13!)^4} \]

6. **Final Result**:
- The number of ways to distribute the 52 cards among 4 players is:
\[ \frac{52!}{(13!)^4} \]