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

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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


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Question ID: mtid-5-stid-8-sqid-2697-qpid-1167