Question:
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:
According to the question,
Number of mice =18,
Number of groups = 3
Since the groups are equally large,
The number of mice in each group can be = 6 mice
The number of ways of placement of mice =18!
For each group the placement of mice = 6!
Hence, the required number of ways = 18!/(6!6!6!)
= 18!/(6!)3