20 players are to be divided into two 10-man teams. In how many ways can that be done?
Say we have a prep school class of fifteen boys.
We partition them into three study groups of five each to study: biology, mathematics, and geography.
This can be done in $\displaystyle \binom{15}{5}\binom{10}{5} \binom{5}{5}=\frac{15!}{(5!)^3} $ ways.
That is an ordered partition because names of the groups as well as the content of the of the group matters.
NOW, We partition them into three teams of five each to play.
This can be done in $\displaystyle \frac{15!}{(5!)^3(3!)} $ ways.
That is an unordered partition because the teams are not named so only the content of the of the team matters.