Results 1 to 4 of 4

Math Help - Combinations

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    12

    Combinations

    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





    Attempt:

    1) No idea. The way I did it seemed to be for permutations. 21x21x5x5x5x5

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

    22 people, 1 president , then there's 21. Choose a vice president. Now 20, and 2 people lef.t

    b) (22,1) * (21,3)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,660
    Thanks
    600
    Hello, Johnboe!

    1) How many 6-letter subsets can you make if 2 are consonants and 4 are vowels"

    The problem is not clearly stated.

    It says subsets, so the order of the letters is not considered.


    If letters may not be repeated in the subsets,
    . . there are: . {21\choose2} choices for the consonants
    . . and {5\choose4} choices for the vowels.

    There are: . 210\cdot5 \:=\:1050 possible subsets.


    If letters may be repeated, it is a very messy problem . . .

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2009
    Posts
    12
    Quote Originally Posted by Soroban View Post
    Hello, Johnboe!


    The problem is not clearly stated.

    It says subsets, so the order of the letters is not considered.


    If letters may not be repeated in the subsets,
    . . there are: . {21\choose2} choices for the consonants
    . . and {5\choose4} choices for the vowels.

    There are: . 210\cdot5 \:=\:1050 possible subsets.


    If letters may be repeated, it is a very messy problem . . .

    Thank you, that is how the answer should be. How is my number 2?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1
    Hello Johnboe
    Quote Originally Posted by Johnboe View Post
    Thank you, that is how the answer should be. How is my number 2?
    Looks fine to me!

    Grandad
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Combinations in a set
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: September 9th 2010, 06:19 AM
  2. How many combinations are possible?
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: July 23rd 2009, 07:53 PM
  3. Combinations
    Posted in the Statistics Forum
    Replies: 2
    Last Post: May 5th 2008, 08:28 AM
  4. How many combinations..?
    Posted in the Algebra Forum
    Replies: 9
    Last Post: May 2nd 2008, 10:34 AM
  5. combinations
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: April 27th 2008, 09:00 AM

Search Tags


/mathhelpforum @mathhelpforum