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How many bit strings of length 12 contain the substring 111000?

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  1. 17 February, 09:58
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    448 strings

    Explanation:

    Each bit string can be filled by two ways either 0 or 1. If the bit strings of length contain the substring '111000' we therefore need a substring of length 6.

    The selection of bits starts from the 1st bit to 7th bit enclosing the substring 111000 and ensuring that the length 6 are all filled. So, there will be 7 ways to contain this substring.

    The total ways to contain this substring = 7*2^6 = 448

    Therefore 448 strings of length 12 contain the substring '111000'.
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