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

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Q. If yeu are deall

4

cards from a shuffled deck of

52

cards, find the probability of getling one queen and three Kings The probatility is

\square

(Round to six decimal places as needed)

Count Queens Draw: Determine the number of ways to draw one queen from the deck. $\newline$ There are $4$ queens in a deck of $52$ cards. So, the number of ways to draw one queen is $4$ .
Count Kings Draw: Determine the number of ways to draw three kings from the deck. $\newline$ There are $4$ kings in a deck of $52$ cards. We need to choose $3$ out of these $4$ kings. The number of ways to do this is given by the combination formula $C(n, k) = \frac{n!}{k!(n-k)!}$ , where $n$ is the total number of items to choose from, $k$ is the number of items to choose, and $!$ denotes factorial. $\newline$ So, the number of ways to draw three kings is $C(4, 3) = \frac{4!}{3!(4-3)!} = 4$ .
Total Cards Draw: Calculate the total number of ways to draw $4$ cards from the deck. $\newline$ The total number of ways to draw $4$ cards from a deck of $52$ is given by the combination formula $C(n, k) = \frac{n!}{k!(n-k)!}$ . $\newline$ So, the total number of ways to draw $4$ cards is $C(52, 4) = \frac{52!}{4!(52-4)!} = \frac{52\times51\times50\times49}{4\times3\times2\times1}$ .
Calculate Probability: Calculate the probability of drawing one queen and three kings. $\newline$ The probability is the number of favorable outcomes divided by the total number of possible outcomes. $\newline$ The number of favorable outcomes is the product of the number of ways to draw one queen and the number of ways to draw three kings, which is $4 \times 4 = 16$ . $\newline$ The total number of possible outcomes is the total number of ways to draw $4$ cards from the deck, which we calculated in the previous step. $\newline$ So, the probability is $\frac{16}{(52 \times 51 \times 50 \times 49) / (4 \times 3 \times 2 \times 1)}$ .
Simplify Probability: Simplify the probability expression and calculate the final answer. $\newline$ The probability is $\frac{16}{\left((52 \times 51 \times 50 \times 49) / (4 \times 3 \times 2 \times 1)\right)}$ . $\newline$ This simplifies to $\frac{16}{(270725)}$ . $\newline$ Now, calculate the decimal value and round to six decimal places as needed. $\newline$ The probability is approximately $0.000059$ .