Q: A field-hockey team played 7 games and won 4 of them.
There were no ties.
a) How many arrangements of the 4 wins and 3 losses are possible?
Is the solution ? . . . . Yes!
Seven games were played: . _ _ _ _ _ _ _
In how many ways can we place the four W's?
Choose 4 of the 7 games: . ways.
b) In how many of these arrangements would the team have at least 2 wins in a row?
The only way in which the team does not have two wins in a row is:
. . . . . one way.
Therefore, there are: . ways to have at least 2 wins in a row.