1. In how many ways can the position of president and secretary of an organization be filled if members A, B, C, and D are eligible for nomination for the 2 positions?

2. In how many ways can the letters of the word FORMULA be rearranged?

3. How many ways are there to select 3 candidates from 8 equally qualified recent graduates for openings in a certain company?

4. A witness to a hit and run accident told the police that the license number contained the letters RLH followed by 3 digits, the first of which is a 5. If the witness cannot recall the last 2 digits, but certain that all 3 digits are different, find the maximum number of automobile registrations that the police may have to check.

5. a) How many ways can 6 people be lined up to get on a bus? b) If a certain 3 persons insist on following each other, how many ways are possible? c) If a certain 2 persons refuse to follow each other, how many ways are possible?