Answer to Question #226271 in Discrete Mathematics for ripon

Question

determine how many bit strings of length can be formed, where three consecutive 0s are not allowed

Answer 1

Let use the following example.

Determine how many bit strings of length 5 can be formed, where three consecutive 0s are not allowed.

The number of elements of the set of different binary strings of length 5 is $2^5=32$ .

$\begin{matrix} 0& 0 & 0 & 0 & 0\\ 0& 0 & 0 & 0 & 1\\ 0& 0 &0 &1 &0 \\ 0& 0 & 0 & 1 & 1 \end{matrix}$

$\begin{matrix} 1 & 0 & 0 & 0 & 0\\ 1 & 0 & 0 & 0 & 1 \end{matrix}$

$\begin{matrix} 0 & 1 & 0 & 0 & 0\\ 1& 1 & 0 & 0 & 0 \end{matrix}$

The number of bit strings of length 5 can be formed, where three consecutive 0s are not allowed, is 32-8=24