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Permutations homework help

  1. Nov 22, 2009 #1
    1. The problem statement, all variables and given/known

    1. The problem statement, all variables and given/known data
    1)How many six letter subsets can you make if 2 are consonants and 4 are vowels.

    2) There are 22 students in the student council and 4 people are to be elected. How many ways can they be elected if:
    a) there must be a vice president and president
    b) vice president is excluded


    2. Relevant equations



    3. The attempt at a solution

    1)
    21x21x5x5x5x5

    Is there a way to do this via combinations?

    2a) C(22,2) * C(2,2)
    b) C(22,3) * C(2,1)


    These are probably horribly wrong, but I am trying. Any help would be appreciated!
     
  2. jcsd
  3. Nov 22, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Re: Combinations

    1) You have not allowed for permutations of the letters chosen. IF all 6 letters are different, then there are 6! ways but you will have to allow for the same two consonants, etc.

    2) First, choose a president. There are 22 ways to do that. Then choose a vice-president. There are 21 ways to do that. Finally choose 2 other members from the 20 remaining students. Permutations of the same students are not relevant.

    3) Again, there are 22 ways to choose a president. Then choose 3 other members from the 21 remaining students. Permutations of the same students are not relevant.
     
  4. Nov 22, 2009 #3
    Re: Combinations

    1) Not quite sure what you mean here.

    2) (22,1) * (21,1) * (20,2) ?

    3) (22,1) * (21,3)
     
  5. Nov 22, 2009 #4
    Re: Combinations

    Anyone? I have a test tomorrow and am unsure :/
     
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