Originally Posted by

**Plato** I am in no way sure that I understand the setup here!

All four different in $1$ way; arrange in $4!$ ways.

Select one to match in $4$ ways, two others in $\dbinom{3}{2}$; arrange in $\dfrac{4!}{2!}$ ways.

Select two to match in $4$ ways $\dbinom{4}{2}$, two others in $\dbinom{3}{2}$; arrange in $\dfrac{4!}{2!\cdot 2!}$ ways.

Select one to match times in $4$ ways ,one others in $3$ ways; arrange in $\dfrac{4!}{3!}$ ways.

Select one to match four times in $4$ ways; arrange in $1$ way.

As to express that in one formula, I have no clue.