Results 1 to 10 of 10

Math Help - No. of ways to paint doors

  1. #1
    Super Member
    Joined
    Dec 2009
    Posts
    755

    No. of ways to paint doors

    A painter is given the job of painting the doors of 5 adjacent bedrooms using 5 colours: red, blue, yellow, green and orange.

    If the owner of the house insists that the doors should be painted with at most two colours, find the number of ways which the painter could have the job done.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,617
    Thanks
    1581
    Awards
    1

    Re: No. of ways to paint doors

    Quote Originally Posted by Punch View Post
    A painter is given the job of painting the doors of 5 adjacent bedrooms using 5 colours: red, blue, yellow, green and orange.
    If the owner of the house insists that the doors should be painted with at most two colours, find the number of ways which the painter could have the job done.
    There are \binom{2+5-1}{2} ways to paint each door. Why?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Dec 2009
    Posts
    755

    Re: No. of ways to paint doors

    Quote Originally Posted by Plato View Post
    There are \binom{2+5-1}{2} ways to paint each door. Why?
    5(6C2)=75, answer is 305
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,617
    Thanks
    1581
    Awards
    1

    Re: No. of ways to paint doors

    Quote Originally Posted by Punch View Post
    5(6C2)=75, answer is 305
    Wouldn't the answer be (15)^5~?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Aug 2011
    Posts
    127

    Re: No. of ways to paint doors

    Punch, note that Plato said that's how many ways there are to paint each door.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member
    Joined
    Mar 2008
    Posts
    934
    Thanks
    33
    Awards
    1

    Re: No. of ways to paint doors

    Quote Originally Posted by Punch View Post
    A painter is given the job of painting the doors of 5 adjacent bedrooms using 5 colours: red, blue, yellow, green and orange.

    If the owner of the house insists that the doors should be painted with at most two colours, find the number of ways which the painter could have the job done.
    I seem to have a different interpretation of this problem than the previous posters.

    It seems to me that you would pick two colors and then paint each door a solid color, using one of the two colors previously selected. So

    \binom{5}{2} \times 2^5

    No multi-color doors for me, please!
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Nov 2011
    Posts
    11

    Re: No. of ways to paint doors

    All the doors can be painted with same color also....
    it says "at most 2 color"
    =no of ways of choosing 1 color *(5 doors) + no of ways of choosing 2 color *(5 doors)
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,617
    Thanks
    1581
    Awards
    1

    Re: No. of ways to paint doors

    Quote Originally Posted by awkward View Post
    I seem to have a different interpretation of this problem than the previous posters.

    It seems to me that you would pick two colors and then paint each door a solid color, using one of the two colors previously selected. So
    \binom{5}{2} \times 2^5
    No multi-color doors for me, please!
    Now that is a possible reading of that problem!
    As many regular readers here may know, I in former life I was an editor for published test questions. As such, when I read a question here I naturally assume it has been fully vetted. However, in this case I think awkward has found what the true meaning of this question: doors have one color.
    That should have been stated.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Super Member
    Joined
    Dec 2009
    Posts
    755

    Re: No. of ways to paint doors

    Quote Originally Posted by awkward View Post
    I seem to have a different interpretation of this problem than the previous posters.

    It seems to me that you would pick two colors and then paint each door a solid color, using one of the two colors previously selected. So

    \binom{5}{2} \times 2^5

    No multi-color doors for me, please!
    That gives 320 and adding the ways of painting all doors in one colour gives 325 ways. But the correct answer is 305.

    I can't seem to spot a correct answer in all the posts.

    And yes, do assume that a door should be painted with only one colour.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Newbie
    Joined
    Nov 2011
    Posts
    11

    Re: No. of ways to paint doors

    Quote Originally Posted by Punch View Post
    That gives 320 and adding the ways of painting all doors in one colour gives 325 ways. But the correct answer is 305.

    I can't seem to spot a correct answer in all the posts.

    And yes, do assume that a door should be painted with only one colour.
    Including akwards post

    Painting with 2 colors

    total no. painting 5 doors with 2 colors = 2^5
    now this combination will also be having case where all the doors were painted same with color...
    no of such cases = 2
    total no. painting 5 doors with 2 colors(choosing 2 colors of 5) = \binom{5}{2}(2^5-2)=300

    Painting with 1 colours


    \binom{5}{1} =5


    so total = 305
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Monty Hall problem with 4 doors
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: November 9th 2011, 04:24 PM
  2. Replies: 5
    Last Post: April 29th 2010, 01:23 PM
  3. Cans of Paint
    Posted in the Algebra Forum
    Replies: 1
    Last Post: April 27th 2009, 04:58 AM
  4. Probability of doors open question
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: January 26th 2009, 11:04 AM

Search Tags


/mathhelpforum @mathhelpforum