Four cards are drawn from a full pack of cards . Find the probability that
all the four are kings,

Answer

To find the probability that all four cards drawn from a full pack of cards are kings, we can follow these steps:

### Step 1: Determine the total number of cards
A standard deck of playing cards contains 52 cards.

### Step 2: Calculate the total number of ways to draw 4 cards from 52
The total number of ways to choose 4 cards from 52 is given by the combination formula:
\[ \text{Total Outcomes} = \binom{52}{4} = \frac{52!}{4!(52-4)!} = \frac{52!}{4! \cdot 48!} \]

### Step 3: Calculate the number of favorable outcomes
In a standard deck, there are 4 kings. The number of ways to choose all 4 kings from these 4 is:
\[ \text{Favorable Outcomes} = \binom{4}{4} = \frac{4!}{4!(4-4)!} = 1 \]

### Step 4: Calculate the probability
The probability of drawing 4 kings is given by the formula:
\[ P(\text{All 4 are Kings}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} = \frac{1}{\binom{52}{4}} \]

### Step 5: Calculate \(\binom{52}{4}\)
Now we need to calculate \(\binom{52}{4}\):
\[ \binom{52}{4} = \frac{52 \times 51 \times 50 \times 49}{4 \times 3 \times 2 \times 1} = \frac{6497400}{24} = 270725 \]

### Step 6: Final probability calculation
Substituting back into the probability formula:
\[ P(\text{All 4 are Kings}) = \frac{1}{270725} \]

### Conclusion
Thus, the probability that all four cards drawn are kings is:
\[ \boxed{\frac{1}{270725}} \]