Question

Three cards are drawn from a pack of 52 cards. Find the chance that all are from the same suit

Answer 1

3 cards can be drawn from a pack of 52 cards in ⁵²C₃ ways.

∴ n(S) = ⁵²C₃

Let event C: All the cards drawn are from the same suit.

A pack of 52 cards consists of 4 suits each containing 13 cards.

∴ 3 cards can be drawn from the same suit in ¹³C₃

∴ n(C) = ¹³C₃ × 4

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

= ${\displaystyle \frac{4\times {}^{13}{\text{C}}_3}{{}^{52}{\text{C}}_3}}$

= ${\displaystyle \frac{4\times 13\times 12\times 11}{52\times 51\times 50}}$

= ${\displaystyle \frac{22}{425}}$