Practice By Tag: COMP 2804: Discrete Structures II

Question: 2017 Winter Final - 8

1 . Consider bitstrings that contain at least one occurrence of 000. Let $S_n$ be the number of such strings having length $n$. Which of the following is true for $n \geq 4$?

(a)

$S_n = S_{n-1} + S_{n-2} + 2^{n-2}$

(b)

$S_n = S_{n-1} + S_{n-2} + S_{n-3} + 2^{n-3}$

(c)

$S_n = S_{n-1} + S_{n-2} + S_{n-3} + 2^{n-4}$

(d)

$S_n = S_{n-1} + S_{n-2} + S_{n-3}$