Solution:

(i) 30!/28!

Using the properties of factorials!

$ 30!/28!=\left( 30\times 29\times 28! \right)/28! $

$ 30!/28!=30\times 29 $

$ 30!/28!=870 $

(ii) (11! – 10!)/9!

Using the properties of factorials, we can write:

11! = 11 × 10 × 9 × …. × 1

10! = 10 × 9 × 8 × … × 1

9! = 9 × 8 × 7 × … × 1

By making use of these values we get,

$ \left( 11!-10! \right)/9!=\left( 11\times 10\times 9!-10\times 9! \right)/9! $

$ \left( 11!-10! \right)/9!=9!\left( 110-10 \right)/9! $

$ \left( 11!-10! \right)/9!=110-10 $

$ \left( 11!-10! \right)/9!=100 $