Two cards are drawn at random from a pack of 52 cards. What is the probability that the drawn cards are both aces?

Q: Two cards are drawn at random from a pack of 52 cards. What is the probability that the drawn cards are both aces?

n(S) = Number of ways of drawing 2 cards out of 52 52C2 = (52 x 51) / (2 x 1) = 1326 n(E) = Number of ways of drawing 2 cards out of 4 = 4C2 = (4 x 3)/2 = 6 ∴ P(E) = 6/1326 = 1/221

1/221
2/13
2/26
None of these

Correct Answer: 1/221

Explanation:

n(S) = Number of ways of drawing 2 cards out of 52
⁵²C₂ = (52 x 51) / (2 x 1) = 1326
n(E) = Number of ways of drawing 2 cards out of 4
= ⁴C₂ = (4 x 3)/2 = 6
∴ P(E) = 6/1326 = 1/221

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