"Your baseball team enters a best out of 7 series. How many different ways can you win in exactly 6 games?"

My attempt was...

-4, 5 or 6 wins out of 6 games

-order doesn't matter

_{6}C_{4}=15

_{6}C_{5}=6

_{6}C_{4}=1

6*15=90... 90 ways?

...but I have a feeling that's not correct since I'm not even sure how to solve these questions anymore. As always, any help is appreciated.

Aleguan
Feb 19, 2018

#1**0 **

I think , since it is best of 7 , you only have to win 4 games, so the win 6 or win 5 scenarios are moot

6 c 4 = 15 is how many ways you can win 4 games in 6 is it not?

ElectricPavlov
Feb 19, 2018

#4**0 **

It is a best of 7 series...so as soon as either team accumulates 4 wins the series is over....so you cannot win 5 games or win 6 games. Clearer now? Hope so....

ElectricPavlov
Feb 19, 2018

#5**+1 **

In this scenario, there are only six games. Your team obtains the fourth win in game six. This means they must have won three of the previous five games. This gives **5C3 = 10** for the number of way this could happen.

GA

GingerAle
Feb 19, 2018

#6**+1 **

Nice catch GA....I missed that 'exactly' word in there ! Thanx Learning.

ElectricPavlov
Feb 19, 2018