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Math Help - Combinations and Probability

  1. #1
    Junior Member
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    Oct 2008
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    Combinations and Probability

    From a standard deck of 52 cards, 2 cards are drawn with out replacement.
    How many combinations of 2 hearts are possible

    would I say 13 C 2 to get 78 is this correct?


    Also if a family has three kids what is the probability of having one boy?

    i know the answer to be 3/8 I did this by writing out each set of possibilities, I was wondering if I am able to do a comb or perm to figure this out.
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  2. #2
    Junior Member
    Joined
    Nov 2008
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    Combinations and Probability

    1. How many combinations of 2 hearts are possible?
    You can draw 1 of 13 the first time, then 1 of the remaining 12 the second time. So I think there would be 13*12 = 156 ways you could daw 2 hearts in two card draws.

    2. Also if a family has three kids what is the probability of having one boy?
    =Number of ways you can have one boy / number of combinations possible

    Number of ways you can have one boy = 3 choose 1 = 3! / (1!*2!) = 3
    Number of combinations possible = 2*2*2 = 8 (A boy or girl each time)
    Answer = 3/8

    I hope this helps.

    - Steve J
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