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"

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

Answer: 3003 ways