# Thread: Tricky Combinations Question - Am I doing it right?

1. ## Tricky Combinations Question - Am I doing it right?

I hate to be asking so many questions one after another but I can't seem to figure any of them out.

Q: A field-hockey team played 7 games and won 4 of them. There were not ties.

a) How many arrangements of the 4 wins and 3 losses are possible? Is the solution 7C4? It matches the answer which is 35.

b) In how many of these arrangements would the team have at least 2 wins in a row?

I'm stumped on this one....

Thanks a lot!

2. 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 $_7C_4$ ? . . . . Yes!

Seven games were played: . _ _ _ _ _ _ _

In how many ways can we place the four W's?

Choose 4 of the 7 games: . $_7C_4 \:=\:35$ 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:
. . $W L\:WL\:WL\:W$ . . . one way.

Therefore, there are: . $35 - 1 \:=\:34$ ways to have at least 2 wins in a row.

3. Thanks for the response! This really clarified my understanding!