Hello, MATHDUDE2!

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 doeshave two wins in a row is:not

. . . . . one way.

Therefore, there are: . ways to have at least 2 wins in a row.