Combinations/Permutations: Series of 7 Games

The Lakers will play the Golden State Warriors in a best of 7 series in which the series ends as soon as any team wins 4 games. The Lakers have a 2/3 chance of winning each game and the Golden State Warriors have a 1/3 chance of winning. What is the probability that the Lakers win the series in exactly six games?

My answer: C(6,4) * (2/3)^4 * (1/3) * (1/3)

However, I am seeing that answer is: C(5,3)* (2/3)^4 * (1/3) * (1/3). Did the book I was given make a mistake because I am confident my answer is right.