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Question

(A) The total number of ways to draw $4$ cards from $52$ is $^{52}C_4$. Alternatively,we can calculate the probability for a specific suit and multipl

Vedclass · Accepted Answer

$\frac{44}{85 	imes 49}$

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(A) The total number of ways to draw $4$ cards from $52$ is $^{52}C_4$. Alternatively,we can calculate the probability for a specific suit and multiply by $4$. The probability that all $4$ cards belong to a specific suit (e.g.,Spades) is: $P = \frac{^{13}C_4}{^{52}C_4} = \frac{13 	imes 12 	imes 11 	imes 10}{52 	imes 51 	imes 50 	imes 49} = \frac{11}{17 	imes 5 	imes 49} = \frac{11}{85 	imes 49}$. Since there are $4$ suits,the total probability is: $4 	imes \frac{11}{85 	imes 49} = \frac{44}{85 	imes 49}$.

Four cards are drawn one by one from a well-shuffled pack of $52$ cards. What is the probability that all four cards belong to the same suit?

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