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

[mr_coffee]

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

 

[mr_coffee]

I think i got it:2^6 - 1 = 63 diffferent symobls

 

[mattmns]

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.

 

[mr_coffee]

Ahh, i c, thanks for the responce, that is probably how they wanted me to figure out the solution because this chapter invovles conbinations.