Question

Two cards are drawn from a pack of 52 cards. Find the probability that both are ace cards.

Answer 1

Two cards can be drawn from a pack of 52 cards in ⁵²C₂ ways.
∴ n(S) = ⁵²C₂
Let C be the event that both the cards drawn are aces.
In a pack of 52 cards, there are 4 ace cards.
∴ 2 ace cards can be drawn from 4 ace cards in ⁴C₂ ways
∴ n(C) = ⁴C₂

∴ P(C) = ${\displaystyle \frac{\text{n}\left(\text{C}\right)}{\text{n}\left(\text{S}\right)}}$

= ${\displaystyle \frac{{}^4{\text{C}}_2}{{}^{52}{\text{C}}_2}}$