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Math Help - Counting Problem - Coin Flip

  1. #1
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    Counting Problem - Coin Flip

    A coin is flipped 10 times. How many outcomes have at most 3 heads?

    My best guess is

    [C(10,3)]+[C(10,2)]+[C(10,1)] = 120 + 45 + 10 = 175 outcomes.

    Is this the solution?
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  2. #2
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    Quote Originally Posted by sedemihcra View Post
    A coin is flipped 10 times. How many outcomes have at most 3 heads?

    My best guess is

    [C(10,3)]+[C(10,2)]+[C(10,1)] = 120 + 45 + 10 = 175 outcomes.

    Is this the solution?
    What about the possibility of all 10 being tails?
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  3. #3
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    Never thought of having all of them being tails. I guess the solution would then be:

    [C(10,3)]+[C(10,2)]+[C(10,1)] + [C(10,0)]
    = 120 + 45 + 10 + 1
    = 176 outcomes.
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  4. #4
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    Yes.

    If the question had been worded...

    For outcomes involving "at least 1 head", how many outcomes contain
    at most 3 heads...


    your first answer was fine.
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  5. #5
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    Thanks a bunch.
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