Permutations/combinations help

  • Context: Undergrad 
  • Thread starter Thread starter roadrunner
  • Start date Start date
Click For Summary
SUMMARY

The discussion focuses on calculating the number of symbols that can be represented in Braille code, where each symbol consists of six dots with at least one dot raised. The correct total is 63, derived from the formula 2^6 - 1, which accounts for all combinations except the case where all dots are down. Additionally, the number of combinations with exactly three raised dots is determined using the binomial coefficient 6C3, resulting in 20. For combinations with an even number of raised dots, the calculation involves summing 6C2, 6C4, and 6C6.

PREREQUISITES
  • Understanding of Braille code and its representation
  • Familiarity with combinatorial mathematics
  • Knowledge of binomial coefficients (nCr)
  • Basic principles of permutations and combinations
NEXT STEPS
  • Study the concept of binomial coefficients in depth
  • Learn about the applications of permutations and combinations in real-world scenarios
  • Explore advanced combinatorial problems and their solutions
  • Investigate the mathematical principles behind Braille and other coding systems
USEFUL FOR

Mathematicians, educators, students studying combinatorics, and anyone interested in the mathematical foundations of coding systems like Braille.

roadrunner
Messages
101
Reaction score
0
permutations/combinations help please

Hello everyone im' stuck on this problem.

It says:
Each symbol in braille code is represened by a rectangular arrangement of six dots. Given that a least 1 dot of the 6 must be raised, how many symbols can be represented in brail?

now i saw this posted somewhere else, they got 63. don't know how.

i got 63 two ways...

2^6-1 (case where all down)=63

6c1+6c2+6c3+6c4+6c5+6c6 -1 also =63 (where 6c3 etc is combinations...6 options choose 3)

can sumone explain how/why that works please.

also part b...how many combinations have EXACTLY 3 raised

and how many have an even number of raised dots
 
Last edited:
Physics news on Phys.org
roadrunner said:
Hello everyone im' stuck on this problem.

How are you stuck? You gave two good answers to the question, both of which are correct and correctly explained. The second approach gives a direct answer to your other questions -- 6 choose 3 ways to have three raised, and the appropriate combinations for only even ones raised.
 
im stuck on part b lol exactly 3 rasied
is is 6c3=20?
and part c...how many symbols have an even number of raised dots...
so 6c2+6c4+6c6?
 

Similar threads

Permutations/combinations with Braille dots
  • · Replies 3 ·
Replies
3
Views
6K
Braille code probabilities homework
  • · Replies 5 ·
Replies
5
Views
4K
Undergrad Can 1/4 of the total combinations match 6 numbers drawn from a set of 80?
  • · Replies 2 ·
Replies
2
Views
7K
High School Solve Combinations Puzzle: 5 Letters ABCDE
  • · Replies 18 ·
Replies
18
Views
3K
MHB Probability of Combinations and Permutations
  • · Replies 4 ·
Replies
4
Views
5K
Undergrad How to answer a Combinations question
  • · Replies 4 ·
Replies
4
Views
2K
Why doesn't (8c1)(13c2) work for choosing a team with at least one woman?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Solving 6-Digit Number Quandaries: 1, 2, 3, 4, 5, 6
  • · Replies 8 ·
Replies
8
Views
7K
Undergrad Combinatorics & probability density
  • · Replies 2 ·
Replies
2
Views
2K
MHB Sara's questions at Yahoo Answers regarding permutations and combinations
  • · Replies 1 ·
Replies
1
Views
2K