I have just done these two questions and I have answers for them but I am not sure if they are correct.
A jazz band is to give one concert in each of nine selected cities. Calculate the total number of orders in which these cities can be visited.
I did this just using $9!$.
The student can select any four out of eight optional modules in semester $1$. And any five out of nine optional modules in semester $2$. Compute the total number of possible module selections for the whole year.
For this is used my calculator and did $\binom{8}{4}+\binom{9}{5}$.
Thank you.
The first number is correct, there are $9!$ permutations of the cities and each permutation corresponds to an order in which they can be visited.
The second one is not correct. The distinction is that for each of the $\binom{8}{4}$ choices in semester 1, we can still make $\binom{9}{5}$ choices in semester 2. So, it should be multiplication rather than addition.