A Coin Flip if a

Question

if a heads is flipped, then the coin is flipped 5 more times and the number of heads flipped is noted; otherwise (i.e., a tails is flipped on the initial flip), then the coin is flipped 3 more times and the result of each flip (i.e., heads or tails) is noted successively. How many possible outcomes are in the sample space of this experiment? 

Answer 1

H H H H H H

H H H H H T

H H H H T H

H H H H T T

H H H T H H

etc maintaining H as the first choice. This results in 32 choices. The first choice is selected and there are 5 other choices, each having 2 possibilities resulting in 2⁵ or 32 possibilities.

Then, when tails is flipped first:

T H H H

T H H T

T H T H

T H T T

etc maintaining T as the first choice. This results in 8 choices. The first choice is selected and there are 3 other choices, each having 2 possibilities resulting in 2³ or 8 possibilities.

32 + 8 = 40 possible outcomes.

One thing that made me scratch my head was the fact that for the initial "heads" case, it states that "the number of heads flipped is noted" while in the case of the initial "tails" case, it states that heads or tails is noted. However, the fact that, in the "heads" case, you are only noting when heads appear does not mean that tails is not a possible outcome.