Significance of rankings of random choices

I have 30 options of food (10 fruit, 10 vegetables, 10 meats), and ask respondents to rank (most favorite to least favorite) 4 randomly selected choices from those options, but always 1 meat, 1 veggie, and 2 fruits. How do I determine statistically significance differences of total most favorite and least favorite, comparing both groups (fruit, veggies, meat) and individual options.

More specifically, how do I do this in SPSS. I'm thinking a linear mixed model or general linear model, or perhaps a multinomial logistic regression, but I'm not sure.