# Counting problem

• Dec 20th 2010, 11:28 AM
Gibo
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?
• Dec 20th 2010, 11:43 AM
Plato
Quote:

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?

$30\cdot 29\cdot\binom{28}{3}$.

Can you explain why that is correct?
• Dec 20th 2010, 12:10 PM
Gibo
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.
• Dec 20th 2010, 12:14 PM
Plato
Quote:

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.
• Dec 20th 2010, 12:17 PM
Gibo
Once again, thanks a lot for your help.