Fh. Five cards are drawn from a standard deck without replacement. What is the probability of that they will be a 10 , jack, queen, king and ace, in that order?

To find the probability of drawing a 10, jack, queen, king, and ace in that specific order from a standard deck of cards without replacement, we can follow these steps: 1. **Identify the total number of cards in the deck**: A standard deck has 52 cards. 2. **Calculate the probability of drawing each card in the specified order**: - The probability of drawing a 10 first: There are 4 tens in the deck, so the probability is \(\frac{4}{52}\). - The probability of drawing a jack second: After drawing a 10, there are 51 cards left, and still 4 jacks, so the probability is \(\frac{4}{51}\). - The probability of drawing a queen third: After drawing a 10 and a jack, there are 50 cards left, and still 4 queens, so the probability is \(\frac{4}{50}\). - The probability of drawing a king fourth: After drawing a 10, jack, and queen, there are 49 cards left, and still 4 kings, so the probability is \(\frac{4}{49}\). - The probability of drawing an ace fifth: After drawing a 10, jack, queen, and king, there are 48 cards left, and still 4 aces, so the probability is \(\frac{4}{48}\). 3. **Multiply the probabilities together**: The overall probability of drawing these cards in that specific order is the product of the individual probabilities. Now, let's calculate this step by step: \[ P = \frac{4}{52} \times \frac{4}{51} \times \frac{4}{50} \times \frac{4}{49} \times \frac{4}{48} \] Now, I will calculate this expression. Calculate the value by following steps: - step0: Calculate: \(\left(\frac{4}{52}\right)\times \frac{4}{51}\left(\frac{4}{50}\right)\times \frac{4}{49}\left(\frac{4}{48}\right)\) - step1: Reduce the fraction: \(\frac{1}{13}\times \frac{4}{51}\left(\frac{4}{50}\right)\times \frac{4}{49}\left(\frac{4}{48}\right)\) - step2: Reduce the fraction: \(\frac{1}{13}\times \frac{4}{51}\times \frac{2}{25}\times \frac{4}{49}\left(\frac{4}{48}\right)\) - step3: Reduce the fraction: \(\frac{1}{13}\times \frac{4}{51}\times \frac{2}{25}\times \frac{4}{49}\times \frac{1}{12}\) - step4: Multiply the terms: \(\frac{4}{663}\times \frac{2}{25}\times \frac{4}{49}\times \frac{1}{12}\) - step5: Multiply the terms: \(\frac{8}{16575}\times \frac{4}{49}\times \frac{1}{12}\) - step6: Multiply the terms: \(\frac{32}{812175}\times \frac{1}{12}\) - step7: Reduce the numbers: \(\frac{8}{812175}\times \frac{1}{3}\) - step8: Multiply the fractions: \(\frac{8}{812175\times 3}\) - step9: Multiply: \(\frac{8}{2436525}\) The probability of drawing a 10, jack, queen, king, and ace in that specific order from a standard deck of cards without replacement is: \[ P = \frac{8}{2436525} \approx 3.283365 \times 10^{-6} \] This means that the probability is approximately \(0.000003283365\), which is a very small probability, indicating that this specific sequence of draws is quite unlikely.