My office mate's sixth grader brought home the following math homework:

Marbles come in 10 colors. There are always seven marbles in a bag, always of seven different colors.
How many bags would you need to be 100% certain of having 10 marbles of the same color?

I logically arrived at 91 marbles clinching it, so 13 bags. 1. Is that correct? 2. In any event, I have no idea how to produce a general equation governing this situation. What is it?

Any assistance is appreciated. I apologize in advance if I have overlooked something glaringly obvious.