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Math Help - Permutations

  1. #1
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    Permutations

    How many permutations of the string ABCDEFG are there where A is somewhere before B?
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  2. #2
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    Quote Originally Posted by alephnull View Post
    How many permutations of the string ABCDEFG are there where A is somewhere before B?
    Here is strong hint: "half the time A comes before B"
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  3. #3
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    P_{n}=n!
    If A is the first letter you have P_{6} posibilities.
    If A is the second letter you have 5 \cdot P_{5} posibilities.
    If A is the third letter you have 4 \cdot P_{5} posibilities.
    If A is the fourth letter you have 3 \cdot P_{5} posibilities.
    If A is the fifth letter you have 2 \cdot P_{5} posibilities.
    If A is the sixth letter you have P_{5} posibilities.
    If A is the seventh letter you have no posibilities.

    So, your answer is P_{6}+5 \cdot P_{5}+4 \cdot P_{5}+3 \cdot P_{5}+2 \cdot P_{5}+P_{5}=6!+5!(5+4+3+2+1)=5!(6+5+4+3+2+1)=5!\cd  ot 21=2520
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