From a well-shuffled deck of 52 cards,13 card | vedclass

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(A) The total number of ways to select $13$ cards from $52$ is $n(U) = \binom{52}{13}$.Let $A$ be the event that the selected $13$ cards contain exact

Vedclass · Accepted Answer

$11/4165$

Vedclass · Answer

(A) The total number of ways to select $13$ cards from $52$ is $n(U) = \binom{52}{13}$.Let $A$ be the event that the selected $13$ cards contain exactly $4$ kings.There are $4$ kings in a deck,and we must select all $4$. The remaining $13 - 4 = 9$ cards must be selected from the remaining $52 - 4 = 48$ non-king cards.Thus,$n(A) = \binom{4}{4} 	imes \binom{48}{9} = \binom{48}{9}$.The probability $P(A) = \frac{n(A)}{n(U)} = \frac{\binom{48}{9}}{\binom{52}{13}}$.$P(A) = \frac{48!}{9!39!} 	imes \frac{13!39!}{52!} = \frac{48! 	imes 13 	imes 12 	imes 11 	imes 10 	imes 9!}{9! 	imes 52 	imes 51 	imes 50 	imes 49 	imes 48!} = \frac{13 	imes 12 	imes 11 	imes 10}{52 	imes 51 	imes 50 	imes 49}$.Simplifying this,we get $P(A) = \frac{11}{4165}$.

From a well-shuffled deck of $52$ cards,$13$ cards are selected at random. The probability that the selected $13$ cards contain exactly $4$ kings is ....

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