As a nice surprise, your mom ordered a pizza with $4$ toppings on it to be delivered to your room. You get the message that it's out for delivery, and you're wondering what she could have possibly gotten you. The pizza place offers $8$ vegetable toppings and $4$ meat toppings.

Out of the $4$ toppings she ordered, suppose your mom got you $2$ veggie toppings. How many different combinations of veggies could this yield? This leaves toppings that must be meat. How many different combinations of meat could this yield?

Out of the $4$ toppings she ordered, suppose your mom got you $3$ veggie toppings. How many different combinations of veggies could this yield? This leaves toppings that must be meat. How many different combinations of meat could this yield?