1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Counting question

  1. Dec 10, 2013 #1
    How many 8 letter words have 3 vowels constants do not repeat.

    Is it
    5^3*26*25*24*23*22 ?
     
  2. jcsd
  3. Dec 10, 2013 #2

    jedishrfu

    Staff: Mentor

    Don't you have to also factor in order too:

    act vs cat vs some nonsense words like tca, cta ...

    cafe vs face
     
  4. Dec 10, 2013 #3
    Another question how do I know when to use the combination equation or permutation equation?
    For instance given the example which is posted above are the following strings the same?

    A E I M N P Q R
    and
    E A I M N P Q R
    They both contain the same three vowels and the only thing I changed was the placement of the first and second terms
     
  5. Dec 10, 2013 #4
    so I should add 8! ?
     
  6. Dec 10, 2013 #5
    I'm not sure that would work, for instance


    A1 B A2
    and
    A2 B A1

    are the same.

    I almost feel like I should add (8 choose 3) instead of 8!
     
  7. Dec 10, 2013 #6

    jedishrfu

    Staff: Mentor

    I think your consonants are unique but your vowels might repeat so you'd also have to factor that in too.
     
  8. Dec 11, 2013 #7

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    You mean multiply by 8!?
    No, your original formula already has some ordering in it.
    For the vowels you have 53, so you've already counted all vowel orders.
    Similarly, for the consonants, you used 26P5, not 26C5, so you have those ordered.
    All that you are missing is integrating the vowels with the consonants. How many ways are there of doing that?
     
  9. Dec 11, 2013 #8

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Remember that the vowels are part of the 26 letters. There are only 21 consonants.
     
  10. Dec 11, 2013 #9

    jedishrfu

    Staff: Mentor

    I missed that, thanks.
     
  11. Dec 11, 2013 #10

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    How true :redface:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted