Three-one strings with matching endpoints

Among binary strings of length 8 that contain exactly three 1s, how many have their first and last bits equal (both 0, or both 1)?

Show hints (2)+
  1. Case on the common endpoint value; only the 6 interior slots are free.
  2. Both ends 1: (61)\binom{6}{1}; both ends 0: (63)\binom{6}{3}; add.

Answer

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26

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Asked at: DRW, Two Sigma

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