Two cards are drawn at random and without replacement from a standard deck of 52 cards. What is the probability that both cards are face cards?

Question: Two cards are drawn at random and without replacement from a standard deck of 52 cards. What is the probability that both cards are face cards?

Solution:
Total card = 52
Total face card = 3 × 4 = 12

Total ways to choose 2 cards from 52 = ⁵²C₂ = (52 × 51)/2 = 1326

Total ways to choose 2 face cards from 12 = ¹²C₂ = (12 × 11)/2 = 66

∴ So, the probability that both cards are face cards = 66/1326
= (2 × 3 × 11)/(2 × 3 × 221)
= 11/221