How many different groupings of 3 pieces of furniture can be chosen for a living room from these three
possibilities: high back chair, low back chair, rocking chair, ottoman, and swivel rocking chair.
A yogurt bar offers walnuts, raisins, blueberries, granola, and honey as toppings. In how many ways can
you choose 3 toppings? In how many ways can you choose 4 toppings?
John has a collection of 15 CDs. Each morning when he drives to work, he takes two of them to play in
his car’s CD player. In how many ways can he make his selection?
In a word game, Ying Par has 7 tiles with 7 different letters on them. How many different sequences of
letters can Ying Par form using 3 of her tiles?
In a word game, Ying Par has 7 tiles with 7 different letters on them. In how many ways can she choose
5 letters to use on her next turn?
In a word game, Ying Par has 7 tiles with 7 different letters on them. On her next turn Ying Par decides
she will trade in 2 of her letters for new ones. In how many ways can she choose the ones to trade in?
How many ways can 5 runners cross the finish line?
A reading list for a course in world literature has 20 books on it. In how many ways can you choose four
books to read?
Ten candidates are running for 3 seats in the student government. You may vote for as many as three
candidates. In how many ways can you vote for those three candidates?
Fifteen students ask to visit a college admissions counselor. Each visit includes one student. In how
many ways can the time slots be assigned?
How many different nine-player batting orders can be chosen from a baseball squad of 16?
How many different teams of 11 players can be chosen from a soccer squad of 16?
Suppose you find seven articles related to the topic of your research paper. In how many ways can you
choose five articles to read?
For a band camp, you can choose two or three roommates from a group of 25 friends. In how many
ways can you choose three roommates?
A salad bar offers eight choices of toppings for lettuce. In how many ways can you choose five
toppings?
How many different orders can you choose to read six of the nine books on your summer reading list?
How many ways are there to choose five shirts out of seven to take to camp?
How many ways can you choose two out of four kinds of flowers for a bouquet?
You must answer exactly 12 out of 15 questions on a test. How many different ways can you select the
questions to answer?
A lab assigns a three-digit identification number to each subject in an experiment. No two subjects
have the same identification. No digit can be repeated in identification. What is the greatest number of
subjects that can be used in the experiment?
Ten people enter a race. In how many ways can first, second, and third places be awarded?
A Colorado license plate has room for seven letters and numbers. Say you were going to make a license
plate with letters ONLY, in which no letters can be repeated. How many different options of license
plates would you have?
You and a friend are playing a game of pool. You only have the pool balls with the numbers 15, 11, 14,
and 8 left to hit in the pocket. In how many different ways can you hit those balls in? What if you had to
hit the 8 ball in last (when you’re playing the game “8-Ball”); how many different ways could you hit the
balls in then?
Your bike combination uses 5 different numbers (no repetition). How many choices for combinations
do you have if you can only use the numbers 0-9?
It’s Christmastime and 7 friends are participating in a Secret Santa gift exchange. All 7 names are
written on separate pieces of paper and placed into a hat. How many different ways can those names
be drawn from the hat?