Question

During a local campaign, eight republicans and five democratic candidates are nominated for president of the school board. If the president is to be one of these candidates, how many possibilities are there for the eventual winner?

Answer 1

Answer:13

Explanation:

Given

During a local campaign 8 republicans and 5 democratic candidates are nominated for president of the school Board.

If the president is to be one of these candidates then

there can be $13^C_1$ ways to select a president

$n^C_r$ can be expanded to $=\frac{n!}{\left ( n-r\right )!\left ( r\right )!}$

therefore $13^C_1=\frac{13!}{\left ( 13-1\right )!\left ( 1\right )!}$

$13^C_1=\frac{13!}{12!\cdot 1!}=13$

Therefore there can be 13 ways to do it.