Question

21. 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?

Answer 1

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!)

$\bold{= 18!/(6!) {}^{3}}$