- #1

cragar

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## Homework Statement

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

how many ways can this be done.

## 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.