1. Four candidates for manager of a department store are ranked according to the weighted average of several criteria. How many different rankings are possible if no two candidates receive the same rank?
2. An examination consists of 12 questions. If 10 questions must be answered, find the number of different orders in which a student can answer the questions.
3. Biologists have identified 4 kinds of small molecules: adenine, cytosine, guanine, and thymine, which link together to form larger molecules in genes. How many 3-molecule chains can be formed if the order of linking is important and each small molecule can occur more than once in a chain?
4. A member of a family of four is asked to rank all members of the family in the order of their power in the family. How many possible rankings are there?