Consider that one way to categorize Pokemon cards is into water type, fire type, and all other types.

3.1. You have a total 21 Pokemons, out of which 7 are water type and 5 are fire type. How many combinations of 3 Pokemon cards (the order they are selected does not matter) exist such that none of the following occurs: a selection has at least two fire types and a selection has at least two water types.

3.2. Your friend sends you 10 random Pokemon cards. How many different combinations exist of their types: water, fire, and other?