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## Homework Statement

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?

## Homework Equations

## 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