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Declan's friend Luka claims that he can read minds. To test Luka's abilities, Declan draws $5$ cards without replacement from a standard deck of $52$ playing cards. Declan then asks Luka to identify in any order which $5$ cards he drew without looking. Assume that Luka has no special abilities and is randomly guessing the cards. What is the probability that Luka correctly identifies all $5$ cards in any order?

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Q. Declan's friend Luka claims that he can read minds. To test Luka's abilities, Declan draws

5

cards without replacement from a standard deck of

52

playing cards. Declan then asks Luka to identify in any order which

5

cards he drew without looking. Assume that Luka has no special abilities and is randomly guessing the cards. What is the probability that Luka correctly identifies all

5

cards in any order?

Calculate Probability First Card: Calculate the probability of Luka guessing the first card correctly. $\newline$ There are $52$ cards in total and Luka needs to guess $1$ card correctly. $\newline$ Probability for the first card = $\frac{1}{52}$ .
Calculate Probability Second Card: Calculate the probability of Luka guessing the second card correctly. $\newline$ After the first card is drawn, there are $51$ cards left and Luka needs to guess $1$ of those correctly. $\newline$ Probability for the second card = $\frac{1}{51}$ .
Calculate Probability Third Card: Calculate the probability of Luka guessing the third card correctly. $\newline$ Now there are $50$ cards left, and Luka needs to guess another one correctly. $\newline$ Probability for the third card = $\frac{1}{50}$ .
Calculate Probability Fourth Card: Calculate the probability of Luka guessing the fourth card correctly. $\newline$ With $49$ cards remaining, Luka guesses one more. $\newline$ Probability for the fourth card = $\frac{1}{49}$ .
Calculate Probability Fifth Card: Calculate the probability of Luka guessing the fifth card correctly. $\newline$ There are $48$ cards left, and Luka makes his final guess. $\newline$ Probability for the fifth card = $\frac{1}{48}$ .
Multiply Individual Probabilities: Multiply all the individual probabilities to find the total probability of Luka guessing all $5$ cards correctly. $\newline$ Total probability = $\frac{1}{52} \times \frac{1}{51} \times \frac{1}{50} \times \frac{1}{49} \times \frac{1}{48}$ .

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