Results 1 to 3 of 3

Math Help - Probability Probelms & Counting Techniques

  1. #1
    Newbie
    Joined
    May 2008
    Posts
    13

    Probability Probelms & Counting Techniques

    How many arrangements of the word ANXIOUS are there if all of the vowels must come first?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,659
    Thanks
    600
    Hello, 16sammy!

    How many arrangements of the word ANXIOUS are there
    if all of the vowels must come first?
    There are 4 vowels: \{A,I,O,U\} and 3 consonants: \{N,S,X\}


    Place the 4 vowels first --- there are: 4! possible arrangements.

    Then place the 3 constants --- there are: 3! possible arrangements.


    Therefore, there are: . (4!)(3!) \:=\:(24)(6) \:=\:\boxed{144 \text{ arrangements}}

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2008
    Posts
    39
    Lets put the vovels first \Rightarrow (AIOU)(NXS)
    So there are 4 \cdot 3 \cdot 2 \cdot 1 different ways of arranging the vovels, and for each vowel arrangement there are  3 \cdot 2 \cdot 1 arrangements of the consonants \Rightarrow \ 4! \cdot 3! different arrangements giving 24 \cdot 6\\=144.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Counting Techniques.
    Posted in the Statistics Forum
    Replies: 3
    Last Post: October 24th 2009, 03:14 PM
  2. Probability Probelms & Counting Techniques
    Posted in the Statistics Forum
    Replies: 11
    Last Post: June 10th 2008, 08:03 PM
  3. Probability Probelms & Counting Techniques
    Posted in the Statistics Forum
    Replies: 1
    Last Post: June 10th 2008, 05:21 PM
  4. Probability Probelms & Counting Techniques
    Posted in the Statistics Forum
    Replies: 2
    Last Post: June 10th 2008, 04:58 PM
  5. probability problem counting techniques.
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: September 27th 2007, 07:50 AM

Search Tags


/mathhelpforum @mathhelpforum