Question

Two teams will play against each other until one of them wins 3 games. How many possibilities there are for this series of games?

A clear explanation will be greatly appreciated.

Answer 1

let W and L represent event of winning and losing by one specific team of two,

Game will end once the team loses or wins 3 games,

total such possibilities are: N(team wins first 3 games)+N(team wins 2 out of first 3 and wins 4th game)+N(team wins 2 out of first 4 games and wins 5th game)+N(team loses first games)+N(team lose 2 out of first 3 and lose 4th game)+N(team lose 2 out of first 4 games and lose 5th game)

=1+³C₂+⁴C₂+1+³C₂+⁴C₂ =1+3+6+1+3+6=20