Results 1 to 4 of 4
Like Tree2Thanks
  • 1 Post By Prove It
  • 1 Post By Soroban

Math Help - Number of ways

  1. #1
    Super Member
    Joined
    Dec 2009
    Posts
    755

    Number of ways

    Ten balls are identical in size and shape of which 2 are red, 3 are blue and 5 are green. The two red balls are labelled as '1' and '2', the three blue balls are labelled '1', '2' and '3', and the five green balls are labelled '1', '2', '3', '4' and '5'. Find the number of ways of choosing 2 balls of identical colours.

    5x4+3x2+2x1=28

    but answer is 14... what is wrong with my workings?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,401
    Thanks
    1273

    Re: Number of ways

    Quote Originally Posted by Punch View Post
    Ten balls are identical in size and shape of which 2 are red, 3 are blue and 5 are green. The two red balls are labelled as '1' and '2', the three blue balls are labelled '1', '2' and '3', and the five green balls are labelled '1', '2', '3', '4' and '5'. Find the number of ways of choosing 2 balls of identical colours.

    5x4+3x2+2x1=28

    but answer is 14... what is wrong with my workings?
    Does the order in which you pick the balls matter? In other words, say I wanted to know how many ways to pick two identical red balls, is choosing 1 then 2 considered a different way than choosing 2 then 1?
    Thanks from Punch
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Dec 2009
    Posts
    755

    Re: Number of ways

    Quote Originally Posted by Prove It View Post
    Does the order in which you pick the balls matter? In other words, say I wanted to know how many ways to pick two identical red balls, is choosing 1 then 2 considered a different way than choosing 2 then 1?
    Right! thanks
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,676
    Thanks
    608

    Re: Number of ways

    Hello, Punch!

    Ten balls are identical in size and shape of which 2 are red, 3 are blue and 5 are green.
    The two red balls are labelled as '1' and '2', the three blue balls are labelled '1', '2' and '3',
    and the five green balls are labelled '1', '2', '3', '4' and '5'.
    Find the number of ways of choosing 2 balls of identical colours.

    5x4 + 3x2 + 2x1 = 28 . permutations?

    but answer is 14 ... what is wrong with my workings?

    Prove It has a legitimate concern.


    You have: . \left(_5P_2\right) + \left(_3P_2\right) + \left(_2P_2) \:=\:20 + 6 + 2 \:=\:28

    Your approach is that choosing (R_1,R_2) in that order
    . . is different from (R_2,R_1) in that order.


    I would assume that the order is not considered.
    The two above outcomes would be considered one outcome: \{R_1,R_2\}

    The answer would be: . \left(_2C_2\right) + \left(_3C_2\right) + \left(_5C_2) \:=\:1 + 3 + 10 \:=\:14
    Thanks from Punch
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: April 10th 2009, 02:03 PM
  2. Replies: 10
    Last Post: April 8th 2009, 11:56 AM
  3. number of ways
    Posted in the Statistics Forum
    Replies: 3
    Last Post: July 24th 2008, 03:23 AM
  4. different number of ways
    Posted in the Statistics Forum
    Replies: 2
    Last Post: July 21st 2008, 02:09 PM
  5. number of ways
    Posted in the Statistics Forum
    Replies: 2
    Last Post: April 19th 2008, 02:54 PM

Search Tags


/mathhelpforum @mathhelpforum