Now arrange the first six vacancies. According to the requirements of the topic, there are 12 cases, so I won't say this.

The seventh power of 1/2 is the probability of a single possible situation, and there are only 12 situations in total, so it is 12 multiplied by the seventh power of 1/2.

As for the 20 you said, it is actually three out of six, (6× 5× 4)/(3× 2× 1) = 20.

In fact, 12 is 20 cases that meet the requirements. 12/20, you said, is based on knowing the three wins and three losses in the first six games and meeting the probability of two consecutive failures. In fact, the overall situation should not be 20, but (7 times of 2) in these seven games, and the answer should be 12/(2

In fact, there are two kinds of algorithm ideas, single probability × times, or all situations that meet the conditions. The reference answer is the first one, and your answer is a misunderstanding of the second one.