2.12. A bus starts with 8 people and stops at 12 locations. (a) In how many ways can the people get off the bus? (That is, how many total "matchings" of people and stops are there?) (b) In how many ways if no 2 people get off at the same stop (that is, if each person gets off at a different stop)?

6 people consisting of 3 couples are seated in a row of 6 chairs to take group pictures.(a) In how many ways could they be seated?(b)How many ways could they be seated if each couple should sit next to each other?Justify your answer.(c) One of the couples broke up and do not want to sit next to each other. Whereas the other 4 want to sit next to their partners. In how many ways could they be seated?

Suppose you are asked to arrange 10 books in a shelf. Three of them are Mathematics, 4 are English books, 2 are History books and the rest are Science books, assuming that books of the same subjects are identical. 1. How many arrangements are possible? 2. Show/draw at least 5 illustrations of these possible arrangements.

A large research project is looking for more researchers. There are 8 spots open on the research team. There are 10 mathematicians and 14 computer scientists that apply for the team. a. How many different ways can a team of 8 be made for the project? b. How many different ways can a team of 8 be made for the project if the team must contain at least one computer scientist and at least one mathematician.