Question

Your class is holding elections to choose a leadership committee of 4 students. If there are 30 students in the class, how many different leadership committees would it be possible to elect?
810,000

27,405

120

657,720

Answer 1

Since order is not important we are only looking for unique combinations of 3, so we need to use the "n choose k" formula.

n!/(k!(n-k)!), n=number of elements to choose from, k is the number of choices made....in this case:

30!/(4!(30-4)!)

30!/(4!*26!)

27405