Question: 2019 Winter Final - 8
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 $m \geq 1$, the number of 00-free bitstrings of length $m$
is equal to the $(m + 2)$-th Fibonacci number $f_{m+2}$.
What is the number of 00-free bitstrings of length 20 that have 1 at position 11 and 0 at position 20? (The positions are numbered $1,2,...,20$.)
What is the number of 00-free bitstrings of length 20 that have 1 at position 11 and 0 at position 20? (The positions are numbered $1,2,...,20$.)
(a)
$f_8 \cdot f_{11}$
(b)
$f_7 \cdot f_{10}$
(c)
$f_9 \cdot f_{12}$
(d)
$f_{10} \cdot f_{12}$