c) Compute the number of ways can Anvi choose salad dressings across five days. Express your answer as a single number.

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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, represent the number of ways Anvi can choose salad dressings across n days, for
n2 0. Find a recurrence relation for a,.
(Hint: consider which dressings she could choose on day n.)
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 five days.
Express your answer as a single number.
Transcribed Image Text: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, represent the number of ways Anvi can choose salad dressings across n days, for n2 0. Find a recurrence relation for a,. (Hint: consider which dressings she could choose on day n.) 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 five days. Express your answer as a single number.
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