how many ways can 17 objects be selected 3 at a time

Answer 1

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.