1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Combinatorics problem

  1. Oct 24, 2016 #1
    1. The problem statement, all variables and given/known data
    The Jones family has 5 boys and 3 girls, and 2 of the girls are twins. In how many ways can they be seated in a row of 8 chairs if the twins insist on sitting together, and their other sister refuses to sit next to either of her sisters?

    2. Relevant equations

    3. The attempt at a solution
    I thought that I could use a "count the complement" technique. First, we would count the the number of ways to just have the two twins paired together. This would be ##2! \cdot 7!## ways. However, this over counts because it includes the pairs where the other sister is adjacent. Thus, we subtract from this ##3! \cdot 6!##, which is the number of arrangements where the other sister is adjacent to the other sisters. This gives 5760. However, this is not the right answer. What am I doing wrong?
  2. jcsd
  3. Oct 24, 2016 #2


    User Avatar
    Gold Member

    You are right about the number of ways to just have the two twins paired together (##2!\times 7!##). But then, to account for the third sister not being adjacent, you have to think more carefully. As a hint, I recommend to treat the three sisters together. Now, how many ways are there to arrange this with the boys? How many about the three sisters together?
  4. Oct 24, 2016 #3


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Please explain your reasoning for that number. Remember, you have already combined the twins into one entity.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Threads - Combinatorics problem Date
Two combinatorics problems Apr 3, 2017
Combinatorics problem Oct 24, 2016
Combinatorics: tennis game with 8 people May 28, 2016
Combinatorics Problem May 13, 2016
Combinatoric problem Feb 1, 2016