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  1. \({5 \choose 2}{11 \choose 6}\) paths.

  2. \({16 \choose 8} - {12 \choose 7}{4 \choose 1}\) paths.

  3. \({5 \choose 2}{11 \choose 6} + {12 \choose 5}{4 \choose 3} - {5 \choose 2}{7 \choose 3}{4 \choose 3}\) paths.

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