18 mice were placed in two experimental groups and one control group, with all groups equally large. In how many ways can the mice be placed into three groups?
18 mice were placed in two experimental groups and one control group, with all groups equally large. In how many ways can the mice be placed into three groups?

Solution:

As per the question,

18 = No. of mice

3 = No. of groups

As the groups are equally large,

No. of mice in each group =6 mice

No. of ways of placement of mice =18!

The placement of mice for each group =6!

As a result, the number of ways required =18 ! /(6 ! 6 ! 6 !) =18 ! /(6 !)^{3}