Question 4: In class, we have seen that for any integer m 1, the number of 00-free bitstrings of length m is equal to fm+2, which is the (m + 2)-th Fibonacci number.

Let n 2 be an integer. For each of the following, justify your answer.

Question 4: In class, we have seen that for any integer m 2 1, the number of 00-free bitstrings of length m is equal to fm+2, which is the (m +2)-th Fibonacci number Let n 2 2 be an integer. For each of the following, justify your answer. How many 00-free bitstrings of length n do not contain any 0? How many 00-free bitstrings of length n have the following property: The rightmost 0 is at position 1 How many 00-free bitstrings of length n have the following property: The rightmost (0 is at position 2 Let k be an integer with 3k Ho many 00-free bitstrings of length n have the following property: The rightmost 0 is at position k. Use the previous results to prove that