Two card are drawn at random from a deck of 52 playing cards. Find the probability of drawing two kings.

Answer

To find the probability of drawing two kings from a standard deck of 52 playing cards, we can follow these steps:

### Step 1: Identify the total number of cards and the number of kings
A standard deck of playing cards contains 52 cards in total. Among these, there are 4 kings (one from each suit: hearts, diamonds, clubs, and spades).

### Step 2: Determine the number of ways to choose 2 kings from the 4 available
We can use the combination formula to find the number of ways to choose 2 kings from the 4 available kings. The combination formula is given by:
\[ nCr = \frac{n!}{r!(n-r)!} \]
For our case, we need to calculate \(4C2\):
\[ 4C2 = \frac{4!}{2!(4-2)!} = \frac{4 \times 3}{2 \times 1} = 6 \]

### Step 3: Determine the total number of ways to choose 2 cards from the 52 cards
Next, we need to calculate the total number of ways to choose 2 cards from the 52 cards. We will use the combination formula again:
\[ 52C2 = \frac{52!}{2!(52-2)!} = \frac{52 \times 51}{2 \times 1} = 1326 \]

### Step 4: Calculate the probability of drawing 2 kings
The probability of drawing 2 kings can be calculated by dividing the number of favorable outcomes (drawing 2 kings) by the total number of outcomes (drawing any 2 cards from 52):
\[ P(\text{2 kings}) = \frac{4C2}{52C2} = \frac{6}{1326} \]

### Step 5: Simplify the probability
Now, we can simplify the fraction:
\[ P(\text{2 kings}) = \frac{6}{1326} = \frac{1}{221} \]

### Final Answer
Thus, the probability of drawing two kings from a deck of 52 playing cards is:
\[ \boxed{\frac{1}{221}} \]