1. ## Counting problem

Hi,
I have some difficulties with this exercise - A claas of 30 school studetns is electing members for the student-stff cimmittee. In how many ways can they elect a president, secretary, and 3 cimmittee members?

2. Originally Posted by Gibo
A claas of 30 school studetns is electing members for the student-stff cimmittee. In how many ways can they elect a president, secretary, and 3 cimmittee members?
$\displaystyle 30\cdot 29\cdot\binom{28}{3}$.

Can you explain why that is correct?

3. Hi,
thanks a lot. I understand that students have 30 options for their first choice, as repetition is not allowed in this case, they have 29 possibilities for the second one and then it comes down to r-combination (repetition is not allowed and order does not matter). At the end we apply the Rule of Product to receive our final answer.

4. Originally Posted by Gibo
I understand that students have 30 options for their first choice, as repetition is not allowed in this case, they have 29 possibilities for the second one and then it comes down to r-combination (repetition is not allowed and order does not matter). At the end we apply the Rule of Product to receive our final answer.
Very good. Yes the Pres and Secretary are ordered and the three other members are not.

5. Once again, thanks a lot for your help.