Rework problem 29 from section 2.3 of your text, involving the selection of officers in an advisory board. Assume that you have a total of 10 people...

Rework problem 29 from section 2.3 of your text, involving the selection of officers in an advisory board. Assume that you have a total of 10 people on the board: 5 out-of-state seniors, 1 in-state senior, 2 out-of-state non-seniors, 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?