William W. answered • 09/01/21

Math and science made easy - learn from a retired engineer

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 2^{5} 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 2^{3} 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.