A train has one engine and six train cars.  Find the total number of ways an engineer can arrange the train. (The engine must be first.)     There are  total ways to arrange the train.

A restaurant offers a choice of 5 salads, 15 main courses, and 9 desserts. How many possible 3-course meals are there?

Twelve people are to have their picture taken as a group. How many arrangements can there be if Mary has to be first in line and Tim last in line? Both Mary and Tim are in the group of twelve.

Bruce has 5 different jackets, 3 pairs of jeans, and 8 pairs of shoes. In how many ways can he choose a jacket, a pair of jeans, and a pair of shoes to wear to tonight’s party?

You volunteer to help drive children at a charity event to the zoo, but you can fit only 7 of the 17 children present in your van. can you drive? How many different groups of 7 children can you drive?