Question

Two cards are randomly from pack of 52 cards. In how many way can 2 be selected such that, (i) both are of heart? (ii) one is king and other is a queen?

Answer 1

In a pack of 52 cards, there are 13 cards of heart. 2 cards of heart out of 13 cards of heart can be selected in ways.

∴ Total combinations = ¹³C₂ × ⁶C₃

= \(\frac{13×12}{2}\)

= 20

(2) In a pack of 52 cards, there are 4 cards of king and 4 cards of queen one card of king out of 4 cards of king can be selected in ⁴C₁ ways and one card of queen out of 4 cards of queen can be selected In ⁴C₁ ways.

∴ Total combinations = ⁴C₁ × ⁴C₁

= 4 × 4

= 16