If 4 cards are selected from a deck of 52 car | vedclass

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Question

(D) The total number of ways to select $4$ cards from $52$ is given by $^{52}C_4$.$^{52}C_4 = \frac{52 	imes 51 	imes 50 	imes 49}{4 	imes 3 	ime

Vedclass · Accepted Answer

$11/4165$

Vedclass · Answer

(D) The total number of ways to select $4$ cards from $52$ is given by $^{52}C_4$.$^{52}C_4 = \frac{52 	imes 51 	imes 50 	imes 49}{4 	imes 3 	imes 2 	imes 1} = 270725$.There are $13$ cards of the suit 'hearts' in a deck.The number of ways to select $4$ cards from these $13$ hearts is $^{13}C_4$.$^{13}C_4 = \frac{13 	imes 12 	imes 11 	imes 10}{4 	imes 3 	imes 2 	imes 1} = 715$.The probability $P$ is given by $\frac{^{13}C_4}{^{52}C_4} = \frac{715}{270725}$.Dividing both numerator and denominator by $65$,we get $\frac{715 \div 65}{270725 \div 65} = \frac{11}{4165}$.

If $4$ cards are selected from a deck of $52$ cards,what is the probability that all cards are of the suit 'hearts'?

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