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 = \[\frac{^{13}{}{C}_5}{^{52}{}{C}_5} = \frac{13 \times 12 \times 11 \times 10 \times 9}{52 \times 51 \times 50 \times 49 \times 48} = \frac{33}{66640}\]