If you are deall $4$ cards from a shuffled deck of $52$ cards, find the probability of getling one queen and three Knys $\newline$ The probatility is $\square$ $\newline$ (Round to six decimal places as needed)

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Q. If you are deall

4

cards from a shuffled deck of

52

cards, find the probability of getling one queen and three Knys

\newline

The probatility is

\square

\newline

(Round to six decimal places as needed)

Determine Queen Selection: Determine the number of ways to choose one queen from the four queens in the deck. $\newline$ There are $4$ queens in a deck of $52$ cards. The number of ways to choose one queen is given by the combination formula $C(n, k) = \frac{n!}{k!(n-k)!}$ , where $n$ is the total number of items, and $k$ is the number of items to choose. $\newline$ So, the number of ways to choose one queen is $C(4, 1) = \frac{4!}{1!(4-1)!} = 4$ .
Determine King Selection: Determine the number of ways to choose three kings from the four kings in the deck. $\newline$ Similarly, there are $4$ kings in a deck of $52$ cards. The number of ways to choose three kings is also given by the combination formula. $\newline$ So, the number of ways to choose three kings is $C(4, 3) = \frac{4!}{3!(4-3)!} = 4$ .
Calculate Total Selection: Calculate the total number of ways to choose the four cards as described (one queen and three kings). $\newline$ The total number of ways to choose the four cards is the product of the number of ways to choose one queen and the number of ways to choose three kings. $\newline$ Total ways = $4$ (for one queen) $\times$ $4$ (for three kings) = $16$ .
Determine Total Ways: Determine the total number of ways to choose any four cards from the deck. $\newline$ The total number of ways to choose any four cards from a deck of $52$ is given by the combination formula $C(52, 4)$ . $\newline$ So, the total number of ways to choose any four cards is $C(52, 4) = \frac{52!}{4!(52-4)!} = \frac{52!}{4!48!} = \frac{52\times51\times50\times49}{4\times3\times2\times1} = 270725$ .
Calculate Probability: Calculate the probability of being dealt one queen and three kings. $\newline$ The probability is the ratio of the number of ways to get the desired hand to the total number of ways to choose any four cards. $\newline$ Probability = Total ways to get one queen and three kings / Total ways to choose any four cards = $\frac{16}{270725}.$
Simplify Probability: Simplify the probability and round to six decimal places as needed. $\newline$ Probability = $\frac{16}{270725} \approx 0.0000591$ (rounded to six decimal places).