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alexmahone
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How many bit strings contain exactly eight 0s and 10 1s if every 0 must be immediately followed by a 1?
Finding the Number of Bit Strings with 8 Zeros and 10 Ones
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Discussion Overview
The discussion revolves around the problem of counting the number of bit strings that contain exactly eight 0s and ten 1s, with the condition that every 0 must be immediately followed by a 1. Participants explore different approaches to solve this combinatorial problem.
Discussion Character
- Mathematical reasoning
- Debate/contested
Main Points Raised
- One participant poses the initial question regarding the arrangement of 0s and 1s under the specified condition.
- Another participant suggests a method for counting the arrangements, proposing that there are 9 positions for the 9th 1 and 8 positions for the 10th 1, leading to a calculation of 72 strings, but later questions this reasoning due to the indistinguishability of the 1s.
- A further contribution outlines a different approach, suggesting that the arrangement can be viewed as having ten objects to arrange, leading to a calculation of $$\dfrac{10!}{8!2!}=45$$.
Areas of Agreement / Disagreement
Participants express differing views on the correct method for counting the bit strings, with no consensus reached on the final answer or the validity of the approaches discussed.
Contextual Notes
Some assumptions about the indistinguishability of the 1s and the arrangement of the 0s and 1s are not fully resolved, leading to different interpretations of the problem.