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Math Help - Permutations involving playing cards

  1. #1
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    Permutations involving playing cards

    Hi I have been given this question:

    Three cards are picked without replacement from a shuffled standard pack of 52 playing cards. What is the probability of picking an ace followed by 2 hearts?

    My attempt: Let omega be a set of ordered sequences of 3 cards drawn without replacement
    |omega|=52x51x50

    Let A be the event of picking an ace followed by 2 hearts
    A=(ace of hearts, heart, heart)+(ace but not ace of hearts, heart, heart)
    How do I calculate |A|?

    Thanks for your help
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  2. #2
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    Re: Permutations involving playing cards

    Quote Originally Posted by yellowcarrotz View Post
    Three cards are picked without replacement from a shuffled standard pack of 52 playing cards. What is the probability of picking an ace followed by 2 hearts?
    My attempt: Let omega be a set of ordered sequences of 3 cards drawn without replacement
    |omega|=52x51x50
    Let A be the event of picking an ace followed by 2 hearts
    A=(ace of hearts, heart, heart)+(ace but not ace of hearts, heart, heart) How do I calculate |A|?
    I will help the one if you do the other and add together.
    \mathcal{P}(\text{ace of hearts, heart, heart})=\frac{(1)(12\cdot 11)}{52\cdot 51\cdot 50}
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  3. #3
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    Re: Permutations involving playing cards

    thanks got it
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