Two cards are drawn randomly from a pack of 52 cards. What is the probability of getting one spade card and one diamond card?

Concept used:

Total number of spade cards = 13

Total number of diamond cards = 13

Formula used:

P = Favorable outcomes/Total outcomes 

Calculation:

Total outcomes = ⁵²C₂ = \(52!\over{(52-2)!2!}\) = \(52 × 51\over 2\) = 1326

Favourable outcomes = ¹³C₁ × 13C1

= 13 × 13 = 169

∴ The Required Probability = 169/1326 = 13/102