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

  1. Oct 27, 2006 #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
     
  2. jcsd
  3. Oct 30, 2006 #2
    I think i got it:


    2^6 - 1 = 63 diffferent symobls
     
  4. Oct 30, 2006 #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.
     
  5. Oct 30, 2006 #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.
     
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