(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

100 hundred people are to be divided into 10 discussion groups with 10 people in each group

how many ways can this be done.

3. The attempt at a solution

So if we think of it as people on a 10 by 10 grid their are 100! ways of populating the grid and then 10! ways or rearranging the columns and 10! ways of rearranging the rows.

so would the answer be

[itex] \frac{100!}{10!^{10}10!} [/itex]

I have 10!^10 because there are ten columns and each of those 10 columns can be arranged 10! ways. And the other 10! on the bottom because I could rearrange those rows 10! ways. And I divide 100! by them because we are over counting. If we switch the people around in the group it is still a distinct group.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Counting problem

**Physics Forums | Science Articles, Homework Help, Discussion**