Hi Jordyn,
The first trick is determining whether you have a combination, where selection order does not matter, or a permutation, where it does. We are not looking at a competition here--i.e. first, second, or third place--nor are we looking at an ensemble such as a menu. So, the order in which the 3 items are selected does not matter.
The formula for combinations:
C(n,r)=n!/r!(n-r)!
where:
n=total number of objects available
r=number of objects selected
!=Factorial, which equates to n*(n-1)*(n-2)....
Thus, for this problem:
n=17
r=3
C(17,3)=17!/(3!14!)
You can plug this into a TI-83 calculator, but I can also show you how to compute by hand if your instructor requires it.
Anyway, from above:
C(17,3)=680
680 different combinations are possible
I hope this helps and good luck.
