I'm having a trouble with a dinner question in Discrete Math:
 
You are preparing soup for the whole family. You have 10 skirrets, 15 tomatoes, N onions, and 3 cabbages. Dad must have a cabbage but is otherwise not picky. Mom hates tomatoes, so she won’t have any of those. Granny dislikes skirrets, tomatoes, and cabbage. You can eat anything.
In how many ways can you prepare dinner for the four people in question, by distributing the veggies? You must give at a minimum of one food item to everyone. How would the answer change if you had to give everyone at least two different vegetables?