Ask Question
7 December, 11:39

induction Consider the set of bitstrings x ∈ {0, 1} n+k with n zeros and k ones with the additional condition that no ones are adjacent. (For n = 3 and k = 2, for example, the legal bitstrings are 00101, 01001, 01010, 10001, 10010, and 10100.) Prove by induction on n that the number of such bitstrings is n+1 k?.

+1
Answers (1)
  1. 7 December, 12:00
    0
    The answer is 6.

    Step-by-step explanation:

    From the question given,

    Let us consider the set of bit strings x ∈ { 0.1} with n zeros and k ones.

    The additional condition that no one are adjacent for n=3 and k=2

    Then

    (n+1 k) = (n+1) ǃ/k ǃ (n+1) ǃ = 4ǃ/2ǃ (2ǃ)

    which is

    n+1 k) = (n+1) ǃ/k ǃ (n+1) ǃ = 4ǃ/2ǃ (2ǃ) = 24ǃ / 2*2 = 24/4

    Therefore

    24ǃ / 2*2 = 24/4 = 6
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “induction Consider the set of bitstrings x ∈ {0, 1} n+k with n zeros and k ones with the additional condition that no ones are adjacent. ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers