Question

Five cards are drawn from a well-shuffled pack of 52 cards. Find the probability that all the five cards are hearts.

Answer 1

Out of 52 cards from a deck, 5 cards can be drawn in ⁵²C₅ ways.
∴ Total number of elementary events = ⁵²C₅
Out of 13 cards of heart, 5 cards can be drawn in ¹³C₅ ways.
∴ Favourable number of events = ¹³C₅
Hence, required probability = $\frac{{}^{13}C_5}{{}^{52}C_5}=\frac{13\times 12\times 11\times 10\times 9}{52\times 51\times 50\times 49\times 48}=\frac{33}{66640}$