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Question
Five cards are drawn from a well-shuffled pack of 52 cards. Find the probability that all the five cards are hearts.
Solution
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 = \[\frac{^{13}{}{C}_5}{^{52}{}{C}_5} = \frac{13 \times 12 \times 11 \times 10 \times 9}{52 \times 51 \times 50 \times 49 \times 48} = \frac{33}{66640}\]
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