Consider how many ways you can get EXACTLY three in a row. That is, no more or no less than three together. We can have four or five Hs, but we have to make sure that only the three are in a row (six Hs will be out because that's clearly not only three in a row).
3 and 3: HHHTTT or TTTHHH or THHHTT or TTHHHT
4 and 2: HHHTHT or HHHTTH or THTHHH or HTTHHH or THHHTH or HTHHHT
5 and 1: HHHTHH or HHTHHH
That's 12 total possibilities where the Hs lie exactly three in a row.
Given that we have six flips, that means we have 2^6 = 64 total possibilities.
Desired outcomes is 12 over total outcomes of 64, or 12/64 = 3/16.
As for the argument about HHHHHH, remember, that HHHHHH is categorically NOT "exactly three heads in a row." The word exactly in GRE terms functions as an "if and only if" in logic: three and only three consecutive heads count. Four consecutives is excluded. Five consecutives is excluded. Six consecutives is excluded.
It is important to be totally precise with the wording on questions like these as this can, as we're seeing, lead to troublesome misinterpretations.
Answer
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