Combinations in Finite
Assume that you have a total of 13 people on the board: 5 out-of-state seniors, 5 in-state seniors, 1 out-of-state non-senior, and 2 in-state non-seniors. University rules require that at least one in-state student and at least one senior hold one of the three offices. Note that if individuals change offices, then a different selection exists.
In how many ways can the officers be chosen while still conforming to University rules?