1) Determine how many ways Brian, Katie, and Charlie can split a 50 dollar dinner bill such that Brian and Katie each pay an odd number of dollars and Charlie pays at least 5 dollars .
2) Determine how many ways I can distribute 80 candies to 3 kids, such that:
The first kid receives an arbitrary number of candies (possibly 0).
The second kid receives an even positive number of candies.
The third kid receives 0, 2, or 5 candies.
Every candy is distributed.
I have been trying to use generating functions to get the answer for these problems, but I am stuck. Any help is greatly appreciated!