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(A) The total number of ways to draw $4$ cards from $52$ cards is given by $^{52}C_{4}$.In a standard deck of $52$ cards,there are $13$ diamonds and $

Vedclass · Accepted Answer

$\frac{^{13}C_{3} 	imes ^{13}C_{1}}{^{52}C_{4}}$

Vedclass · Answer

(A) The total number of ways to draw $4$ cards from $52$ cards is given by $^{52}C_{4}$.In a standard deck of $52$ cards,there are $13$ diamonds and $13$ spades.The number of ways to select $3$ diamonds from $13$ is $^{13}C_{3}$.The number of ways to select $1$ spade from $13$ is $^{13}C_{1}$.Therefore,the number of favorable outcomes is $^{13}C_{3} 	imes ^{13}C_{1}$.The probability is the ratio of favorable outcomes to total outcomes:$P = \frac{^{13}C_{3} 	imes ^{13}C_{1}}{^{52}C_{4}}$.

$4$ cards are drawn from a well-shuffled deck of $52$ cards. What is the probability of obtaining $3$ diamonds and $1$ spade?

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