**1)** how many bit string of length 12 contain at least three 1s?

**2)** A coin is flipped 10 times where each flip comes up either heads or tails. how many possible outcomes contain at most three tails?

**3)** thirteen people on a softball team show up for a game. How many ways are there to choose 10 players to take the field?

**4)** a club has 25 members. How many ways are there to choose four members of the club to serve on an executive committee?

**5)** how many ways are there for a horse race with four horses to finish if ties are possible? (any number of the four horses may tie).