+0

Combinatorics Problem

+1
847
6
+119

"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
6C4=15
6C5=6
6C4=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.

Feb 19, 2018

#1
+19863
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?

Feb 19, 2018
#2
+4330
0

I think you're correct, EP.

tertre  Feb 19, 2018
#3
+119
0

I'm sorry, I don't understand what you mean...

Aleguan  Feb 19, 2018
#4
+19863
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
+1821
+2

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

Feb 19, 2018
#6
+19863
+1

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

ElectricPavlov  Feb 19, 2018