From a well shuffled pack of 52 playing cards, two cards are drawn together at random. What is the probability that both of the drawn cards are kings?

Introduction / Context:
This problem checks understanding of basic probability with playing cards and the use of combinations when two cards are drawn together without replacement. The focus is on counting how many ways we can obtain two kings from a standard deck and comparing this to the total number of possible pairs of cards.

Given Data / Assumptions:

• There is a standard deck with 52 cards.
• The deck contains 4 kings in total.
• Two cards are drawn together without replacement.
• All unordered pairs of cards are equally likely.
• We want the probability that both selected cards are kings.

Concept / Approach:
When several objects are drawn together and order does not matter, combinations are used. The probability of an event is equal to the number of favourable combinations divided by the total number of possible combinations. Here, favourable outcomes are all 2 card combinations that consist of kings only, and the total outcomes are all 2 card combinations from the full deck of 52 cards.

Step-by-Step Solution:
Total number of ways to choose any 2 cards from 52 is C(52, 2). C(52, 2) = 52 * 51 / 2 = 1326 possible pairs. Number of kings in the deck is 4. Number of ways to choose 2 kings from these 4 is C(4, 2). C(4, 2) = 4 * 3 / 2 = 6 favourable pairs. Required probability = favourable pairs / total pairs = 6 / 1326. Simplify 6 / 1326 by dividing numerator and denominator by 6 to get 1 / 221.

Verification / Alternative check:
An alternative method is to compute the probability sequentially. The probability that the first card is a king is 4 / 52. Once this happens, 3 kings remain out of 51 cards, so the probability that the second card is also a king is 3 / 51. The combined probability is (4 / 52) * (3 / 51) which equals 12 / 2652. After simplification this again reduces to 1 / 221, confirming the combination based result.

Why Other Options Are Wrong:
1/15 is far too large and would correspond to many more favourable outcomes than actually possible. 1/26 would mean 51 favourable pairs, which does not match the count of 6 ways to choose two kings. 2/221 is larger than the correct probability and does not result from any valid combination count.

Common Pitfalls:
Learners often confuse combinations and permutations by accidentally counting the pair king of hearts followed by king of spades as different from king of spades followed by king of hearts, even though the question treats both as the same pair. Another frequent error is to divide by 52 * 51 instead of C(52, 2), which corresponds to treating order as important when it is not. Always match the counting method to the wording of the question, especially when cards are drawn together.

Final Answer:
The probability that both cards drawn are kings is 1/221.