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Math Help - probability

  1. #1
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    probability

    Mr and Mrs Zimmerman want to give their baby a name so that the baby's 3 initials are in alphabetical order.
    how many different initials could the baby end up with? (for example B,G,Z is acceptable but G,B,Z is not etc.)

    all i can think of is that there are 26 letters in the alphabet and 26 choose 3 = 2600, but how many of these groups of 3 letters are in alphabetical order?
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  2. #2
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    Re: probability

    Quote Originally Posted by amyl95 View Post
    Mr and Mrs Zimmerman want to give their baby a name so that the baby's 3 initials are in alphabetical order. how many different initials could the baby end up with? (for example B,G,Z is acceptable but G,B,Z is not etc.)
    all i can think of is that there are 26 letters in the alphabet and 26 choose 3 = 2600, but how many of these groups of 3 letters are in alphabetical order?
    I suppose that we will follow the western world's custom and the Zimmerman's child will have the third initial, Z
    But surely the child could be named Adan Abraham Zimmerman, AAZ.
    You seem to assume the initials are different. WHY?
    Why not Zeno Zerox Zimmerman, ZZZ?

    There are \binom{2+26-1}{2} ways to have an alpha string of length two in alphabetical order.
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