# Combination and Permutation Problem

I'm trying to calculate total possible unique potential combinations.  I'm trying to solve for a tv dinner tray with 4 little sections for one each of:  meat, veggie, starch, dessert.  These sections don't change.  In other words, the meat always goes in the meat section, the veggie in the veggie section, and so on.

What makes this more complex is we have different types of meats/veggies/starches/desserts and uneven amounts of the individual foods.

For instance, we have a fridge stocked with:
Meats: 5 servings of chicken, 2 servings fish, 1 serving pork, 7 servings steak
Veggie: 8 servings broccoli, 2 servings kale, 5 servings carrot
Starch: 7 servings potatoes, 3 servings pastas, 2 servings rice, 3 servings yams
Desserts: 5 servings apple pies, 5 servings cherry pies, 5 servings ice creams

How can I calculate the unique combinations possible? I am trying to determine how to create this formula so I will know if I add a carrot or take one away to know how many potential unique combinations there are left. By unique I mean that no 2 tv dinners look the same.  This is an example where they all total 15 but there are many examples where we will run out of meats and still have other categories left over even before duplicates are considered.  If they all had the same quantity it would be rather easy to calculate total unique combos but with different amounts of each item within categories it appears there needs to be a more complex formula to determine total unique tray possibilities.  That is the formula I am looking for an answer to.

• There is something missing which is : if a person wants to eat only veggie ? Or everyone needs to take one item from each section ?

• “This is an example where they all total 15” I assume you mean servings?

• This problem is not properly stated, I'm afraid. Can you try to explain better? How many servings is a meal composed of and do they need to be all different?

• Everyone needs to take one item from each section. There is always a meat in the meat section always a veggie in the veggie section. Every meal is composed of 1 serving of each section. In my example i have 15 total servings (but of different types of each category) but it doesnt always work out that way. Sometimes we only have 12 servings of meats (maybe 4 chicken 3 fish 2 pork 4 steak).

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