Discrete maths problem-counting

  • Context: Undergrad 
  • Thread starter Thread starter tc
  • Start date Start date
  • Tags Tags
    Discrete
Click For Summary
SUMMARY

The discussion focuses on calculating the number of bit strings of length 8 that contain either three consecutive 0s or four consecutive 1s using the principle of inclusion-exclusion. The method involves adding the count of strings with three consecutive 0s to those with four consecutive 1s, while subtracting the overlap where both conditions are met. This approach provides a systematic way to solve the problem efficiently.

PREREQUISITES
  • Understanding of discrete mathematics principles
  • Familiarity with the inclusion-exclusion principle
  • Basic knowledge of combinatorial counting techniques
  • Ability to analyze binary strings and their properties
NEXT STEPS
  • Study the inclusion-exclusion principle in depth
  • Explore combinatorial counting methods for binary strings
  • Learn about generating functions for counting sequences
  • Investigate applications of discrete mathematics in computer science
USEFUL FOR

Students of discrete mathematics, computer scientists, and anyone interested in combinatorial problem-solving techniques.

tc
Messages
7
Reaction score
0
how many bit strings of length 8 contain either three consecutive 0s or four consecutive 1s?
 
Mathematics news on Phys.org
As ever inclusion-exclusion: the number with 3 consecutive 0s plus the number with 4 consecutive 1s over counts by how many?
 

Similar threads

Help me understand this question -- "Three consecutive zeros" in a binary string
  • · Replies 3 ·
Replies
3
Views
2K
Counting number of consecutive elt's in nit string
  • · Replies 2 ·
Replies
2
Views
2K
High School Needing advice for winning/doing well in a Math Counts competition
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Can you help me mathematically describe this pattern?
  • · Replies 6 ·
Replies
6
Views
3K
Recurrence Relation for Two Consecutive 0s in Ternary Strings
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Count and Categorical Variables...
  • · Replies 3 ·
Replies
3
Views
2K
Figuring out Natural Deduction problem but can't find mistake
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Basically it's easy to solve the problems given recursive formulas (repost)
  • · Replies 2 ·
Replies
2
Views
2K
In discrete Math Adv Counting Techniques - see picture - h
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Hard problem from Bay Area Math Meet
  • · Replies 8 ·
Replies
8
Views
4K