In a series of seven games, the first team to win four games wins the series. Both the team have equal probability of winning one game. What is the probability that the team that wins the first game will win the series?
My answer: in case of zero losses: 1/8
in case of one loss: 3/16 in case of two losses: 6/32 in case of three losses: 10/64
And then you just add them up. The only thing is that the book's answer for two losses is 5/32. Since there are four positions for losses and you are choosing two, it should be 6 according to me.
Where am I going wrong?