Question

An election ballot asks voters to se4five city commissioners from a group of fifteen candidates. In how many wsys can this be done

Answer 1

That's "15 choose 5"

`\displaystyle{15 \choose 5} = (15! )/(5! 10!) = (15 \cdot 14 \cdot 13 \cdot 12 \cdot 11)/(5 \cdot 4 \cdot 3 \cdot 2 \cdot 1) = (15/(5(3))(14/2)(13)(12/4)(11)\\\\= 7(13)(3)(11)=231(13)=3003`

Answer: 3003 ways