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Thread: 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 $\displaystyle \frac{1}{5}$ (1/5 *4/4*3/3)

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

    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 $\displaystyle (5)(4)(3)=60$ possible three letter words.
    There are $\displaystyle D(4)(3)=12$ 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 $\displaystyle (5)(4)(3)=60$ possible three letter words.
    There are $\displaystyle D(4)(3)=12$ that begin with D.
    thus the probability of making a word that begins with D is $\displaystyle \frac{12}{60}$

    how do I show this using permutations, though?

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

    I know the numerator is 12 since $\displaystyle _{5}P_{3}$ = 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 $\displaystyle \frac{12}{60}$ YES
    I just need to use another permutation for the numerator.
    Because D has be used, you have $\displaystyle _4 P_2 =12 $
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  5. #5
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    Ah ok. Thanks
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