Results 1 to 3 of 3

Math Help - permutations - too many balls!

  1. #1
    Member
    Joined
    May 2009
    Posts
    91

    Question permutations - too many balls!

    Hi folks,

    I thougth I could do these permutation questions until now!

    I have 6 balls, 3 red, 1 blue, 1 brown, and 1 green. In how many ways can I arrange them in a line? In how many of these arrangements will no two red balls come together?

    The first part is fairly standard i.e arrangements of n things with p things of the same kind gives n! / p! arrangements:

    6! / 3! = 6 x 5 x 4 = 120.

    The second part would be easy too if there were only 2 red balls. We would consider the two like objects as a single object so there would be 5 objects arranged in 5! ways and since the two red balls can be arranged in 2! ways amoung themselves, we would have 2.5! arrangements with the two balls together, so

    120 (total perms) - 2.5! (arrangements in which the two red balls are together) = arrangements in which the two red balls are not together.

    But this 3rd red ball is the problem! I tried the obvious, namely joining the 3 red balls to produce 4 entities i.e. 4! arrangements with 3! arrangements of the 3 red balls so that:

    total perms - 4!3! = arrangements with no three red balls together

    but then I noticed that I am asked to find how many arrangements with no two red balls together. I also not clear on whether total perms is 6! or 6!/3!
    6!/3! - 4!/3! is a negative so something is definitely wrong!

    Any ideas?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,969
    Thanks
    1788
    Awards
    1
    Quote Originally Posted by s_ingram View Post
    I have 6 balls, 3 red, 1 blue, 1 brown, and 1 green. In how many of these arrangements will no two red balls come together?
    The three odd balls make four possible places for the red balls:_Bl_Br_G_.
    So there \binom{4}{3}=4 ways to place the red balls.
    But the string _Bl_Br_G_ can be arranged in 3!=6 way.
    So how many is that total?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    May 2009
    Posts
    91
    Yep, that's the right answer. Seems I was on the wrong track completely. Thanks again.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: October 7th 2011, 05:58 PM
  2. Balls in a bag
    Posted in the Statistics Forum
    Replies: 1
    Last Post: March 6th 2011, 05:44 PM
  3. a basket contains 5 red balls, 3 blue balls, 1 green balls
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: May 28th 2010, 03:39 AM
  4. Balls in an Urn
    Posted in the Statistics Forum
    Replies: 8
    Last Post: October 31st 2009, 11:23 AM
  5. how many balls
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: June 19th 2007, 10:16 AM

Search Tags


/mathhelpforum @mathhelpforum