Question

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

Answer 1

$18$ mice can be arranged among themselves in ${18}_{P_{18}}$$=18!$ ways.

There are three groups and each group is equally large.

So $18$ mice are divided in three groups and they can be arranged amongst themselves inside the group.

Therefore the number of ways mice placed $18!$ to three groups are $=\frac{18!}{6!6!6!}$

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