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Math Help - Permutation Simple Question

  1. #1
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    Permutation Simple Question

    "How many permutations exist of the letters in the word COMPUTER?"

    I said 8! because there are 8 letters and so it should just be n! where n is the number of choices. Right?

    "How many permutations end in a vowel?"


    I thought 7!3! but I'm not certain. Because there are 3 vowels and I want one of them in the last position, and the other 7 letters can be whatever else is left..

    Is this correct? If not, can someone tell me what I am doing wrong?
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  2. #2
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    Quote Originally Posted by mander View Post
    "How many permutations exist of the letters in the word COMPUTER?"

    I said 8! because there are 8 letters and so it should just be n! where n is the number of choices. Right?

    "How many permutations end in a vowel?"

    I thought 7!3! but I'm not certain. Because there are 3 vowels and I want one of them in the last position, and the other 7 letters can be whatever else is left..

    Is this correct? If not, can someone tell me what I am doing wrong?
    How many end in E?
    How many end in U?
    How many end in O?

    How many does that make?

    RonL
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  3. #3
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    I don't know how to figure that out.
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  4. #4
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    Quote Originally Posted by mander View Post
    I don't know how to figure that out.
    If it ends in E how many letters are there in front of the E that can re-arrange .....? etc.
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  5. #5
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    7... Or is this a trick question? I already said 7 though..
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  6. #6
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    Quote Originally Posted by mander View Post
    7... Or is this a trick question? I already said 7 though..
    How many end in E + How many end in U + How many end in O \neq7! \, 3! \, .......
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  7. #7
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    Yes, but I implied there were 7 choices before the vowel and was wondering about the vowel part specifically, which is why I said 7! originally... it was the 3! that wasn't sitting well with me. There's a miscommunication here, and I'm sorry for that.

    anyway, I am going with 7! * C(3,1) ... I will check with someone in math lab tomorrow. Sorry for wasting your time...
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  8. #8
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    Quote Originally Posted by mander View Post
    Yes, but I implied there were 7 choices before the vowel and was wondering about the vowel part specifically, which is why I said 7! originally... it was the 3! that wasn't sitting well with me. There's a miscommunication here, and I'm sorry for that.

    anyway, I am going with 7! * C(3,1) ... I will check with someone in math lab tomorrow. Sorry for wasting your time...
    How many end in E: 7!
    How many end in U: 7!
    How many end in O: 7!

    Total: 7! + 7! + 7! = 3*7!

    This is actually the same as 7! * C(3,1) but I'm not sure that you got the correct answer for the correct reason.
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  9. #9
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    hi

    Hi!

    Isnt this a combination of "k-permutations" and the addition principle.

    How many end in E?
    If we subtract the letter E from the rest of the letters we have 7 left.
    And seven letters can be permutated in 7! ways.

    The same goes for O and U.

    So 7! + 7! + 7! = 15120 ways of permutating the word COMPUTER when the word ends with a vowel.

    If the question was "How many ways can the word be permutated and DONT end with a vowel?" You would just take the total permutations 8! = 40320
    and subtract 15120

    40320 - 15120 = 25 200

    I HOPE this is right, I am very very new at discrete math though.
    Plz correct me if Im wrong.
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  10. #10
    Grand Panjandrum
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    Quote Originally Posted by mr fantastic View Post
    How many end in E: 7!
    How many end in U: 7!
    How many end in O: 7!

    Total: 7! + 7! + 7! = 3*7!

    This is actually the same as 7! * C(3,1) but I'm not sure that you got the correct answer for the correct reason.
    Amazing that's what I was just thinking

    RonL
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