If you can choose one item from a group of $a$a items and a second item from a group of $b$b items, what is the total number of two-item choices?

The number of possible permutations of $r$r objects taken from $n$n items is $\nPr{n}{r}$nPr. Express this in factorial form.

The number of possible combinations of $r$r objects taken from $n$n items is $\nCr{n}{r}$nCr. Express this in factorial form.

Evaluate $\frac{\nPr{8}{3}}{3!}-\nCr{8}{3}$8P33!−8C3.

Use permutations and combinations