q4 discrete math open response

4. Anvi's Salad Answer the following questions on recurrence relations: a) Suppose Anvi eats a salad for lunch every day. She picks exactly one salad dressing each time, and she always picks one of Ranch, Caesar, or Balsamic. She follows two rules: . She never has Balsamic two days in a row . If she picks Caesar, then she must have picked Ranch on the previous day. Let a,I represent the number of ways Anvi can choose salad dressings across :1 days, for n 2 0. Find a recurrence relation for an. (Hint: consider which dressings she could choose on day :1.) b) What are the initial conditions for the recurrence relation from part (a)? For full credit, you must use the fewest necessary for your recurrence. {Note: she cannot choose Caesar on day 1 since there is no previous day to choose ranch.) c) Compute the number of ways can Anvi choose salad dressings across ve days. Express your answer as a single number