Clarification of a concept in Permutation Statement 1
No. of ways in which $(m+n+p)!$ different things can be divivded into different groups containing m,n & p things respectively. is $(m+n+p)!/m!n!p!$ 
Statement 2
If $m=n=p$ and the groups have identical qualititive characteristic then the no. of groups=$(3n)!/(n!)^3*3!)$
How this '$3!$' arrives? Why doesnot substituting the values work in statement 2?

It is because the groups are identical in statement $1$ and identical in statement $2$ that the difference arises.
The difference can be seen in the following example:
There is exactly $1$ way to split a group of three people into three groups of size $1$, $\frac{3!}{1!1!1!3!}$. However if each group is distinct there are $6$ ways to split them, $\frac{3!}{1!1!1!}$
