An election ballot ask voters to select four city commissioner from a group of twelve candidates. In how many ways can this be done?

Expert Answers
lfryerda eNotes educator| Certified Educator

Since the order of the selection doesn't matter (that is the first and second commissioner are the same selection as the second and first), this is a combination question.  There are twelve possibilities and selecting four from those twelve is

`12C4`

`={12!}/{8!4!}`   cancel out the 8!

`={12 times 11 times 10 times 9}/{4 times 3 times 2 times 1}`   now simplify

`=11 times 5 times 9`

`=495`

There are 495 ways to make the selection.