Hi,

If anyone can please check what I have done, that would be awesome,

70.

**Cross Country****:** There are three schools competing in a cross country race. School A has six runners. School B has five runners. School C has four runners. For scoring purposes, the race only considers the school of each runner. How many different finishing orders are there for the fifteen runners?

I'm not quite sure how to do this. I believe the answer is 15!, but I am not sure.

Mr F says: $\displaystyle {\color{red}\frac{15!}{6! \cdot 5! \cdot 4! }}$. **Newspaper:** Your school has an editor in chief, and an assistant editor in chief. The staff of the newspaper has twelve students. In how many ways can students be chosen for these two positions? A combination is used to solve the problem. There are 66 ways that students can be chosen for the two positions.

Mr F says: Since the order is important (Mary as chief and Bob as Assistant is different to Bob as Chief and Mary as Assistant) it's a permutations problem: $\displaystyle {\color{red}^{12}P_2}$. **Student Council:** Five representatives from a senior class of 280 students can be chosen to represent student council. In how many ways can students be chosen to represent student council?

Mr F says: Since the order is not important it's a combinations problem: $\displaystyle {\color{red}^{280}C_5}$.
Thank you very much

Isabel