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45 sequences. Make it easier and think what are the 2 tail flips. They are: 1-2; 1-3;1-4...1-10. That is 9 sequences starting with 1. There are 9 sequences starting with 2, 9 starting with 3, etc, up to 10. That makes 90 sequences, but since 1-2 is the same as 2-1, ie order doesn't matter, divide that in half to get 45.

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