Question

An art gallery has eight new paintings, all the same size, but enough room on the wall for six of them. How many ways can the director arrange the eights paintings on the wall?
28
48
20,160
40,320

Answer 1

That would be 8P6  = 20160 answer

Answer 2

The order matters.

$k$ objects can be chosen out of $n$ objects, when the order matters, in $P(n,k)=\dfrac{n!}{(n-k)!}$ ways.

So, the answer is $P(8,6)=\dfrac{8!}{2!}=3\cdot4\cdot5\cdot6\cdot7\cdot8=20,160$ ways.