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Introduction to the product rule

  1. Feb 26, 2008 #1
    1. The problem statement, all variables and given/known data

    a) How many bit strings are there of length 8?

    b) How many bit strings are there of length 8 which begins with 2 1's?

    2. Relevant equations

    Product Rule

    3. The attempt at a solution

    a) Since a bit string is either 0 or 1 there are two possibilities for each one. By the rule of products 2^8 = 256 bit strings.

    c) the first two choices are fixed so its 11(0/1)(0/1)(0/1)(0/1)(0/1)(0/1)

    2^6 = 64 possible different bit strings.

    when u allow the preceding 1 to change u basically double the 64 combinations and allowing the first one u quadruple it getting back to the original 256.


    Could someone please confirm my result. Danke!
     
  2. jcsd
  3. Feb 26, 2008 #2
    In short: Yes.
     
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