Question

Five cards arc 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 ${}^{52}{C}_5$ ways.

$\therefore$ Total number of elementary events =${}^{52}{C}_5$

Out of 13 cards of heart, 5 cards can be drawn in =${}^{13}{C}_5$ ways.

$\therefore$ Favourable number of events = ${}^{13}{C}_5$

Hence, required probability = $\frac{{}^{13}{C}_5}{{}^{52}{C}_5}$

$=\frac{13\times 12\times 11\times 10\times 9}{52\times 51\times 50\times 49\times 48}=\frac{33}{66640}$