Suppose Anna hosts a cookout with 7 of her friends. She has purchased 8 burgers, 8 steaks, and 5 pieces of chicken. If she wants to cook 16 food items in total (each person gets two items), including at least 2 burgers and 1 steak, how many possibilities are there to choose from what she purchased? Do not distinguish between who gets what, only consider the 16 food items.

(a) Solve using inclusion-exclusion.

(b) Solve using a generating function.

(C) What if two people want 3 food items, and the rest want 2 (and there are still at least 2 burgers and 1 piece of chicken among those cooked)?

(d) What if four people want 2 food items, and the rest only want 1 (and there are still at least 2 burgers and 1 piece of chicken among those cooked)?