Question

6. (10 pts) What is the general form of the solution of a linear homogeneous recurrence relation if its characteristic equation has roots 2, 2, 3, 4, 4, 4, 4?

7. (10 pts) Nine people (Ann, Ben, Cal, Dot, Ed, Fran, Gail, Hal, and Ida) are in a room. Five of them stand in a row for a picture. In how many ways can this be done if Ann and Ben must be in the picture but not standing next to each other?

8. (10 pts) How many positive integers not exceeding 1000 are divisible by 4, 6, or 9? Compute all the way to the final answer – a single number.

9. (7 pts) A professor puts 4 different keys on a round keychain. In how many ways can four keys be placed on the keychain?

Answer 1