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Math Help - permutation question

  1. #1
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    permutation question

    if you have the letters A,B,C,D,E and you form 3 letter "words" with these letters, what is the probability that the word starts with D?

    how do I show this using permutations?

    using fractions I know the answer is \frac{1}{5} (1/5 *4/4*3/3)

    so it would be \frac{something}{_{5}P_{3}}

    how do I show the number of possible combinations that begin with D as a permutation?
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  2. #2
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    Quote Originally Posted by hello View Post
    if you have the letters A,B,C,D,E and you form 3 letter "words" with these letters, what is the probability that the word starts with D?
    I assume that you mean three different letters.
    There are (5)(4)(3)=60 possible three letter words.
    There are D(4)(3)=12 that begin with D.
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  3. #3
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    Quote Originally Posted by Plato View Post
    I assume that you mean three different letters.
    There are (5)(4)(3)=60 possible three letter words.
    There are D(4)(3)=12 that begin with D.
    thus the probability of making a word that begins with D is \frac{12}{60}

    how do I show this using permutations, though?

    \frac{possibilities with D as first letter}{_{5}P_{3}}

    I know the numerator is 12 since _{5}P_{3} = 60

    I just need to use another permutation for the numerator. Sorry if my OP was confusing
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  4. #4
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    Quote Originally Posted by hello View Post
    thus the probability of making a word that begins with D is \frac{12}{60} YES
    I just need to use another permutation for the numerator.
    Because D has be used, you have _4 P_2 =12
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  5. #5
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    Ah ok. Thanks
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