Question

If you divide 6! by 4! you are evaluating P(6, 4)

Answer 1

When you're evaluating P(n, k), you are essentially saying there are n objects and you will need to arrange them in k spaces.

This is essentially the same as: $^{6}P_4$, which follows the formula:

$P(6, 4) = ^{6}P_4 = \frac{6!}{(6 - 4)!} = \frac{6!}{2!}$
If you're dividing by 4!, you are evaluating P(6, 2)