A poker hand consists of 5 cards drawn at ran | vedclass

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Question

(A) The total number of ways to choose $5$ cards from $52$ is $^{52}C_5 = 2598960$.To form a full house (a pair and a triple):$1$. Choose the face val

Vedclass · Accepted Answer

$\frac{6}{4165}$

Vedclass · Answer

(A) The total number of ways to choose $5$ cards from $52$ is $^{52}C_5 = 2598960$.To form a full house (a pair and a triple):$1$. Choose the face value for the triple: $^{13}C_1 = 13$ ways.$2$. Choose $3$ cards of that face value: $^4C_3 = 4$ ways.$3$. Choose the face value for the pair from the remaining $12$ values: $^{12}C_1 = 12$ ways.$4$. Choose $2$ cards of that face value: $^4C_2 = 6$ ways.Total favorable outcomes = $13 	imes 4 	imes 12 	imes 6 = 3744$.Probability = $\frac{3744}{2598960} = \frac{6}{4165}$.

$A$ poker hand consists of $5$ cards drawn at random from a well-shuffled pack of $52$ cards. The probability that a poker hand consists of a pair and a triple of equal face values (for example, $2$ sevens and $3$ kings or $2$ aces and $3$ queens, etc.) is:

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