Marvin the fly starts at $(0,0).$ Each step, Marvin moves one unit right or one unit up. He is trying to get to the point $(5,7)$. However, at $(4,4)$ there is a frog that will eat him if he goes through that point. In how many ways can Marvin reach $(5,7)$?

I run a book club with $n$ people, not including myself. Every day, for $365$ days, I invite three members in the club to review a book. What is the smallest positive integer $n$ so that I can avoid ever having the exact same group of three members over all $365$ days?


How many ways can you distribute $4$ different balls among $4$ different boxes?

How many ways can you distribute $4$ identical balls among $4$ identical boxes?


How many ways can you distribute $4$ identical balls among $4$ different boxes?


How many ways can you distribute $4$ different balls among $4$ identical boxes?

There are ten people in the Baking Club, including Mark. They choose $3$ people to form an executive committee.


There are ten people in the Baking Club, including Mark. They choose $3$ people to form an executive committee.

How many possible committees can be formed that do not include Mark?