Counting 8-bit strings

How many 88-bit binary strings (each character 00 or 11) either begin with a 11 or end with the two characters 0000 (or both)?

Show hints (2)+
  1. Count "begins with 1" and "ends with 00" separately by fixing those bits.
  2. Subtract the strings satisfying both (inclusion–exclusion).

Answer

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160

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Asked at: Jane Street, Citadel

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