Confused, how many symbols can be represented by braille code? Combinations wee

In summary, the question asks how many symbols can be represented in braille given that at least one dot out of six must be raised. The two possible solutions are 2^6 - 1 = 63 and using the combination formula to find the sum of all possible combinations of raised dots.
  • #1
mr_coffee
1,629
1
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?

I'm thinking I have to use combinations becuase the multipcation rule won't work..the combination formula is the following:

Choosing r items out of n,

n!/r!(n-r)!

So I can choose 6 symbols, but if at least one has to be raised, that means all 6 can be raised, so would i have 12 possibilites?

then i was thinking maybe the total possilbites of r items would be
2^12 because the dot is either up or down.

So would the answer be 2^12 = 4096 symbols?

That seems way too big...
so the other answer might be:

12!/2!(10)! = 66. that sounds more like it but I'm still not sure if its correct.

Any help would be great
 
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  • #2
I think i got it:2^6 - 1 = 63 diffferent symobls
 
  • #3
That looks good (the 2^6 - 1 = 63).

Another way to do it is the following: Partition the symbols by how many dots are raised up. We can have 1 dot raised up, of which there are 6 choose 1 possible symbols. We can have 2 dots raised up, of which there are 6 choose 2 symbols, and so on (up to 6 dots raised up). The sum of these yields 63 total possible symbols.
 
  • #4
Ahh, i c, thanks for the responce, that is probably how they wanted me to figure out the solution because this chapter invovles conbinations.
 

Related to Confused, how many symbols can be represented by braille code? Combinations wee

1. What is braille code and how does it work?

Braille code is a tactile writing system used by individuals with visual impairments. It consists of patterns of raised dots that represent letters, numbers, punctuation, and other symbols. These dots are read by running one's fingers over them from left to right.

2. How many symbols can be represented by braille code?

The basic braille code consists of 64 possible symbols, also known as cells. These cells can be combined to represent a wide range of characters, including letters, numbers, punctuation, and even special symbols and contractions.

3. What are the different combinations of braille code?

There are different combinations of braille code, including single-cell, two-cell, three-cell, and four-cell combinations. Single-cell combinations represent the most basic braille symbols, while multi-cell combinations are used for more complex characters or contractions.

4. Is there a limit to the number of symbols that can be represented by braille code?

Technically, there is no limit to the number of symbols that can be represented by braille code. With the use of different combinations and contractions, braille code can represent any character or symbol found in written language.

5. How long does it take to learn braille code?

The time it takes to learn braille code varies for each individual. Some factors that can affect the learning process include a person's age, level of vision impairment, and previous exposure to braille. On average, it can take several months to learn the basic braille code and longer for more advanced combinations and contractions.

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