If you are dealt 5 cards from a shuffled deck of 52​ cards, find the probability of getting two queens and three kings.The probability is nothing.​(Round to six decimal places as​ needed.)

The probability of getting two queens and three kings is [tex]\frac{1}{1082900}[/tex]Solution:Given that, you are dealt five cards from a shuffled deck of 52 cards  We have to find the probability of getting two queens and three kings  Now, we know that, in a deck of 52 cards, we will have 4 queens and 4 kings.[tex]{ probability }=\frac{\text { favarable possibilities }}{\text { number of possibilities }}[/tex]Probability of first queen:[tex]\text { Probability for } 1^{\text {st }} \text { queen }=\frac{4}{52}=\frac{1}{13}[/tex]Probability of second queen:[tex]\text { Probability for } 2^{\text {nd }} \text { queen }=\frac{3}{51}=\frac{1}{17}[/tex]Here we used 3 for favourable outcome, since we already drew 1 queen out of 4And now number of outcomes = 52 – 1 = 51Probability for first king:[tex]\text { Probability of } 1^{\text {st }} \text { king }=\frac{4}{50}=\frac{2}{25}[/tex]Here favourable outcomes = 4And now number of outcomes = 51 – 1 = 50Probability for second king:[tex]\text { Probability of second king }=\frac{3}{49}[/tex]Here favourable outcomes = 3, since we already drew 1 kingAnd now number of outcomes = 50 - 1 = 49Probability for third king:[tex]\text { Probability of third king }=\frac{2}{48}=\frac{1}{24}[/tex]Here favourable outcomes = 2, since we already drew 2 king And now number of outcomes = 49 - 1 = 48Now the total probability of getting 2 queens and 3 kings from a shuffled deck of cards is:[tex]=\frac{1}{13} \times \frac{1}{17} \times \frac{2}{25} \times \frac{3}{49} \times \frac{1}{24}=\frac{1}{1082900}[/tex]Hence, the probability is [tex]\frac{1}{1082900}[/tex]