why is the answer option (c)?, i dont understand the math, how do i solve future problems like this?

A bitstring is called 00-free, if it does not contain two 0's next to each other. In class, we have seen that for any m1, the number of 00 -free bitstrings of length m is equal to the (m+2)-th Fibonacci number fm+2. What is the number of 00-free bitstrings of length 55 that have 0 at position 9 , and 1 at position 40? (The positions are numbered 1,2,,55.) (a) f7f29f15 (b) f8f30f16 (c) f9f31f17 (d) f10f32f18