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Permutations/combinations help

  1. Sep 14, 2007 #1
    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. jcsd
  3. Sep 14, 2007 #2


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    Homework Helper

    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.
  4. Sep 14, 2007 #3
    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???
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