1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    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!

How many ways to put 100 distinguishable particles into 6 boxes?

  1. Oct 16, 2013 #1
    1. The problem statement, all variables and given/known data
    An adsorbing filter allows gas particles to stick to locations
    on the filter surface. Once a particle sticks to a location, that
    location is filled. The filter can no longer remove gas particles
    when all locations are filled. Each 1.0 nm 2 of the filter surface
    has six adsorbing locations, each capable of adsorbing one gas
    particle. In the volume just adjacent to one 1.0 nm 2 area, there
    are 100 gas particles. Each of these particles has a slightly dif-
    ferent energy, making each particle unique. In how many ways
    can these 100 particles adsorb onto the six locations?


    2. Relevant equations



    3. The attempt at a solution
    Consider first 6 particles. You can put the first particle in one of 6 boxes, the second particle in one of 5 remaining boxes, etc., which gives 6! ways to put 6 particles into 6 boxes.

    Consider 7 particles. The excluded particle can be thought of as being in the "excluded" box, so you get 7! ways to put 7 distinguishable particles into 6 boxes.

    Consider 8 particles. You still have 6! ways to put 6 particles in the 6 boxes. Multiply this by the number of ways can you can put 2 particles out of 8 into the "excluded" box. This latter number is 8 X 7, so the total number of ways to put 8 distinguishable particles into 6 boxes is
    6! X 7 X 8 = 8!.

    For 9 particles, I think you can have 7 X 8 X 9 ways to put 3 distinguishable particles out of 9 into the "excluded" box, so the total number of ways to put 9 distinguishable particles into 6 boxes is
    6! X 7 X 8 X9 = 9!

    Following this logic, the total number of ways to put 100 distinguishable particles into 6 boxes is 100!.

    Is this correct? Or am I missing something?
    thanks
     
  2. jcsd
  3. Oct 16, 2013 #2
    The problem statement says that each box can accommodate only one particle. This problem requires you to find the number of combinations of 100 items taken 6 at a time.
     
  4. Oct 16, 2013 #3
    Not to sound redundant, but the key word here is: combinations
     
  5. Oct 17, 2013 #4
    So if I get your drift, then the number of 6-element subsets (where the order of the 6 elements doesn't matter) in a set of 100 distinguishable elements would be 100 choose 6, which is 1.2 X 10^9. Is that the idea?
    thanks
     
  6. Oct 17, 2013 #5

    DrClaude

    User Avatar

    Staff: Mentor

    I have a different on the question. For me, the use of "how many ways" implies that it matters which particle is where on the filter.
     
  7. Oct 17, 2013 #6
    Yes. This is the correct answer.
     
  8. Oct 17, 2013 #7

    DrClaude

    User Avatar

    Staff: Mentor

    As I said above, I disagree. I don't think this is what the problem is asking.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: How many ways to put 100 distinguishable particles into 6 boxes?
Loading...