You are correct with respect to any given series. For a fair coin "HHHHHHHHHH" is as likely as "HHTHTTTHTH". For distributions of results in the aggregate, however, the head-to-tail ratio should be about 1-to-1. (For a any roll of a pair of fair dice, they should total 7 about 1 out of every 6.) So based on the known properties of a coin, the probability of observing a series containing 10 heads (~.09%) is far less than the probability of observing a series containing 5 heads and 5 tails (~24.6%).
But this is not the issue when deciding whether chance events can result in complexity. You could make a character count of a computer program and list the relative frequencies of the characters, but that would tell you nothing about the nature of the program or its operation. It is the sequence that matters.
the other thing that needs to be considered is selection. Nature, for whatever reasons, favors certain sequences. It is as if a dice player could always keep his winnings and always rule losing tosses "invalid".
the "whatever reasons" part is not arbitrary, but is the subject of study.