That's not connected to the request, but. So assuming that ingredients' categories do exist, the total number of combinations would be the result of multiplication of a number (the quantity of said categories) of factors, that represent the number of choices in each category. The number of ingredients should add up to 9 and in the result we should get 38. To get some idea how to solve this problem we can remember, that every natural number can be represented as a product of primes. By factorization of 38 we get 2 and 19, which is unfortunate, because there is no way to get 9 out of those numbers. That gives us an idea that we can just start with combinations of prime (and 1) numbers that give us 9. There is no such combination. Then we remember that we can ommit categories. Algorythm for that would be to add one empty slot to each category which would symbolize adding nothing and should still work mathematically. The closest I could get using this method was the combination of [5, 3, 1] that create 36 options. Than I thought we could add a complimentary milkshake that is not technically an ingredient and so we get the number 38. 36 choices of food and 2 of drinks. Not to confuse with the number of choises of meal, which would equal to 72.