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three cards are randomly drawn from a standard deck of $52$ cards, without replacement. find the probability that the first card is spades, the second card is hearts, and the third card is spades.

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Final answer:

To find the probability of drawing three specific cards from a standard deck without replacement, we can multiply the probabilities of each event happening. Overall probability = 169/26,300.

Step-by-step explanation:

To find the probability of drawing three specific cards from a standard deck without replacement, we can multiply the probabilities of each event happening. Let's assume the events A, B, and C represent the first card being spades, the second card being hearts, and the third card being spades, respectively.

The probability of event A happening is 13/52 since there are 13 spades in the deck. After the first card is drawn, there are 51 cards left, and now there are 13 hearts in the deck. So, the probability of event B happening is 13/51.

After the second card is drawn, there are 50 cards left, and there are still 13 spades in the deck. Therefore, the probability of event C happening is 13/50. Finally, we can multiply these probabilities together to find the overall probability: (13/52) * (13/51) * (13/50) = 169/26,300.

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