# Permutations/combinations help

1. Sep 14, 2007

permutations/combinations help plz

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: Sep 14, 2007
2. Sep 14, 2007

### CRGreathouse

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.

3. Sep 14, 2007