Question

1. The Stanley Cup Finals in Hockey or the NBA Finals in Badminton continue until either the representative team form the Western Conference or from the Eastern Conference wins 4 games. How many different orders are possible (WW EEEE means that the Eastern team won in 6 games) if the series goes

a) 4 games?

b) 5 games?

c) 6 games?

d) 7 games?

Answer 1

a)

number of different orders , if series goes on 4 games =N( Eastern Conference wins 1st 4 games)+N( Eastern Conference loses 1st 4 games) =1+1 =2 (WWW ,EEEE)

b)

number of different orders , if series goes on 5 games =N(wins 4th game on 5th)+N(loses 4th game on 5th)=N(arrangement of 3 wins in first 4)+N(arrangement of 3 loses in first 4)

=C(4,3)+C(4,3)

=4+4 =8

c)

number of different orders , if series goes on 6 games =N(arrangement of 3 wins in first 5)+N(arrangement of 3 loses in first 5)

=C(5,3)+C(5,3)

=10+10

=20

d)

number of different orders , if series goes on 7 games =N(arrangement of 3 wins in first 6)+N(arrangement of 3 loses in first 6)

=C(6,3)+C(6,3)

=20+20

=40