How many possible menus can be created with 10 foods from 4 categories?

[majorlag]

I need help on how to solve these homework problems.

1. Coefficient of x^12 in (1+x^2)(1-x)^-10


2.Find a generating function for the problem: there are 4 food categories, each category comprising of 20 distinct foods. Ten foods with at least one from each category is to be selected. how many menus are possible?

 

[matt grime]

1. Just do it; you know the expansion of (1-x)^{-10} and that is all that you need.

 

[majorlag]

is the answer C(22,10)?