A man draws two cards together from a pack of 52 cards. What is the…

For selecting a group of items without replacement, the classical probability of an event E is P(E) = n(E) / n(S), where n(S) is the total number of equally likely ways to select the group (given by the combination formula, nCr = n! / (r!(n−r)!)) and n(E) is the number of those ways that satisfy the desired condition.

1. Total sample space: the number of ways to choose any 2 cards from the 52-card deck is 52C2 = (52 × 51) / 2 = 1326.

2. Favourable outcomes: the number of ways to choose 2 kings from the 4 kings in the deck is 4C2 = (4 × 3) / 2 = 6.

3. Probability: P(E) = n(E)/n(S) = 6 / 1326 = 1/221.

Independent check: computing the probability sequentially without replacement gives the same result — P(first card is a king) = 4/52, and P(second card is a king given the first was a king) = 3/51, so P(both kings) = (4/52) × (3/51) = 12/2652 = 1/221, confirming the combination-based answer.