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

1 Answer

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lfryerda | High School Teacher | (Level 2) Educator

Posted on

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


`={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`


There are 495 ways to make the selection.