In an experiment, a fair coin is tossed 8 times and the face that appears ($H$ for head or $T$ for tail) for each toss is recorded.

How many elements of the sample space will have no tails?

How many elements of the sample space will have exactly one tail?

How many elements of the sample space will start or end (or both) with a tail and have a total of exactly two tails?

How many elements of the sample space will start or end with a tail and have an adjacent pair or triple of tails and include a total of exactly three tails?