I am a novice at discrete mathematics and I have been working on trying to get my combinatorical skills up and i was working on some practice questions for permutation practice and i came across this question that is seemingly simple but i dont know how to do this.
A school election is to be heard for 3 faculty and 2 student seats. The faculty with the highest votes gets three years contract, second highest gets two years and the third highest gets a year. Each student seat is for a year. If there are 9 faculty members and 7 students on the ballot, how many different election results are possible assuming that ties do not occur.
I tried calculating the r-combination and adding and multiplying them to see if i get the answer. However, i have had no success.
The answer is 10,584 and i dont know how to get it.