I'm not sure how switch / case fits into this. You don't need it (unless this is part of a homework assignment and it requires you to use a switch / case.) Let's define the food groups. I'm using string arrays but you could use numbers.
meat = ["chicken"; "beef"; "pork"; "lamb"];
veggie = ["beans"; "peas"; "corn"];
fruit = ["apple"; "pear"; "blueberry"];
Use ndgrid to generate the 3-D arrays where combining the same element of each of the three arrays gives you one combination.
[M, V, F] = ndgrid(meat, veggie, fruit);
Combine them into a 2-D list with each row representing one combination.
possibleDinners = [M(:), V(:), F(:)];
What to eat today?
whichDinner = randi(size(possibleDinners, 1));
dinnerTonight = possibleDinners(whichDinner, :)