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Math Problems
Algebra 1
Permutations
At a dog show, a German Shepherd, a Golden Retriever, a Dachshund, a Boxer, an Airedale, an Alaskan Malamute, and a Basset Hound won first place in their divisions. In how many different orders could these winners be announced?
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Gabriel's favorite snack just became available in
3
3
3
new flavors, and he wants to try each of the new flavors one after the other.
\newline
In how many unique orders can Gabriel arrange the new flavors?
\newline
◻
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All that Cody has left of his Halloween candy stash is one pack each of dark chocolate squares, jawbreakers, hard candies, and gummy bears. In how many different orders can he eat the remaining candy?
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Arianna, Xavier, and Rebecca have been invited to a dinner party. If they each drive there separately, in how many different orders can they arrive?
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At a dog show, first-place winners were selected in each of
4
4
4
divisions. In how many different orders could these winners be announced?
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An online auction site includes listings for
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4
4
items. If the listings all close at different times, in how many different orders could the listings close?
\newline
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_
_
_
\_\_\_\_
____
orders
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A restaurateur is planning a new menu. If
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4
4
appetizers will be offered, in how many different orders can they be listed on the menu?
\newline
_____ orders
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A florist is working on a wedding bouquet that uses
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3
3
different types of flowers. In how many different orders can the various types of flowers be added to the bouquet?
\newline
_
_
_
_
\_\_\_\_
____
orders
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Sophie works at a bakery. She needs to restock the containers of
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4
different colors of sprinkles. In how many different orders can she restock the containers?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
orders
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If
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3
teams are playing in the same sports league, in how many different orders can they finish their season?
\newline
_____ orders
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Kirk and his friends are trying out a new restaurant together. They've ordered
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5
5
dishes. If the dishes all arrive separately, in how many different orders could their dishes arrive?
\newline
_
_
_
_
\_\_\_\_
____
orders
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There are
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4
puppies standing in a row at puppy obedience school. In how many different orders could they be lined up?
\newline
_
_
_
_
\_\_\_\_
____
orders
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Dustin, a competitive athlete, is figuring out which races to sign up for next year. There are many types of races to choose from, including
5
K
5\text{K}
5
K
runs, century rides, and ultramarathons. If Dustin signs up to complete one of each type, in how many different orders could he complete them?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
orders
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Bruce is raising chickens in a backyard coop. If he is expecting
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4
new chicks to hatch, in how many different orders can they hatch from their eggs?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
orders
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Hugo, who is a huge fan of the Summer Olympics, always records his favorite events. One week, he recorded a total of
4
4
4
events. In how many different orders could he watch these events?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
orders
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Hannah makes a smoothie for breakfast every morning. Today, she wants to use
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5
different fruits. In how many different orders can she add these fruits to her blender?
\newline
_
_
_
_
\_\_\_\_
____
orders
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An auctioneer is preparing to auction off
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5
items as part of an estate sale. In how many different orders can she present the items at the auction?
\newline
_____ orders
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Dirk, a competitive athlete, is figuring out which races to sign up for next year. There are many types of races to choose from, including
50
50
50
-kilometer trail runs, double century rides, and sprint triathlons. If Dirk signs up to complete one of each type, in how many different orders could he complete them?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
orders
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A magician is preparing for a show by unpacking his box of props. He will need
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4
different props for the show. In how many different orders can they be unpacked?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
orders
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Spencer is arranging cheeses in a row on a cheese board. The cheeses he has are Roquefort, Limburger, Gruyere, and Gouda. In how many different orders can Spencer arrange them?
\newline
_____ orders
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Varsity Pizza offers onions, mushrooms, sausage, oregano, and basil on their pizzas. Each server working at Varsity Pizza needs to be able to recite all of the toppings offered. In how many different orders could a server recite the toppings?
\newline
_____ orders
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A grocery store wants to place a row of candy at the check-out counter. If the cashier has one box each of
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4
4
different types of candy, in how many different orders can the boxes of candy be arranged?
\newline
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_
_
_
_
\_\_\_\_\_
_____
orders
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Jackie only has
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4
4
pieces of Halloween candy left. In how many different orders can she eat the remaining candy?
\newline
_
_
_
_
\_\_\_\_
____
orders
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A celebrity chef is writing a new cookbook and is deciding how to organize the
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5
entree recipes. In how many different orders could they appear?
\newline
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_
_
_
_
\_\_\_\_\_
_____
orders
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Some architecture students are viewing photographs of buildings built in Greek Revival, Medieval, and Romanesque styles, with one photograph per style. In how many different orders could the styles be viewed?
\newline
_____ orders
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A celebrity chef is writing a new cookbook and is deciding how to organize the
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3
3
entree recipes. In how many different orders could they appear?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
orders
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Dylan is opening his own restaurant and needs to design the menus. If he will be offering
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3
3
entrees, in how many different orders could the entrees be listed on the menu?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
orders
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A grocery store wants to place a row of candy at the check-out counter. If the cashier has one box each of
3
3
3
different types of candy, in how many different orders can the boxes of candy be arranged?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
orders
Get tutor help
Stanley wants to plant
5
5
5
different types of flowers in his garden this year. If he plants one type of flower each morning, in how many different orders could the flowers be planted?
\newline
_____ orders
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A magician is preparing for a show by unpacking her box of props. She will need
4
4
4
different props for the show. In how many different orders can they be unpacked?
\newline
_
_
_
_
\_\_\_\_
____
orders
Get tutor help
A candy shop is unveiling a new line of candies made with real fruit juice. The candy will be available in
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3
flavors. If they want to release one new flavor every week, in how many different orders can the flavors be released?
\newline
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_
_
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_
\_\_\_\_\_
_____
orders
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A group of
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4
4
friends have been invited to a dinner party. If they each drive there separately, in how many different orders can they arrive?
\newline
_
_
_
_
\_\_\_\_
____
orders
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Brooke is putting
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4
tools into a toolbox, one at a time. In how many different orders could she add them?
\newline
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_
\_\_\_\_
____
orders
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The cheerleading squad is holding a car wash to raise money. Already,
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parents have promised to come have their cars washed. In how many different orders can their cars show up?
\newline
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_
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_
\_\_\_\_\_
_____
orders
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Greenpoint City Diner is introducing a new dessert menu, which includes
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5
different desserts. In how many different orders could the desserts be listed on the menu?
\newline
_____ orders
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At a big sale on shoes, Isabelle picks out
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5
pairs of shoes. In how many different orders could she try them on?
\newline
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_
\_\_\_
___
orders
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Logan, who has a black belt in karate and kung fu, is practicing for an upcoming belt promotion test. During practice, he wants to run through the
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4
weapon forms he knows. In how many different orders could Logan practice these forms?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
orders
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Leroy, who has a black belt in karate and kung fu, is practicing for an upcoming belt promotion test. During practice, he wants to run through the
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4
4
weapon forms he knows. In how many different orders could Leroy practice these forms?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
orders
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An ice cream parlor has a handwritten sign listing the flavors available each day. If there are
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flavors available today, in how many different orders can they be listed?
\newline
_
_
_
_
\_\_\_\_
____
orders
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A group of
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4
guests attend a red carpet event. If they each pose for the cameras separately, in how many different orders can they have their pictures taken?
\newline
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\_\_\_\_
____
orders
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Aaron is a high school student who wants to learn about various college majors. Aaron plans to look up Spanish, Journalism, Biology, and Physics in a book of majors. In how many different orders could he look up these majors?
\newline
_____ orders
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Hugo is opening his own restaurant and needs to design the menus. If he will be offering
3
3
3
entrees, in how many different orders could the entrees be listed on the menu?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
orders
Get tutor help
Sanjay, who is a huge fan of the Summer Olympics, always records his favorite events. One week, he recorded a total of
5
5
5
events. In how many different orders could he watch these events?
\newline
_____ orders
Get tutor help
At a dog show, first-place winners were selected in each of
3
3
3
divisions. In how many different orders could these winners be announced?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
orders
Get tutor help
The top
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4
students have made it to the final round of judging in the school science fair competition. In how many different orders can the judges rank their posters?
\newline
_
_
_
_
\_\_\_\_
____
orders
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Donald and his friends are trying out a new restaurant together. They've ordered
4
4
4
dishes. If the dishes all arrive separately, in how many different orders could their dishes arrive?
\newline
_
_
_
_
\_\_\_\_
____
orders
Get tutor help
At a dog show, first-place winners were selected in each of
5
5
5
divisions. In how many different orders could these winners be announced?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
orders
Get tutor help
Tisha makes a smoothie for breakfast every morning. Today, she wants to use
3
3
3
different fruits. In how many different orders can she add these fruits to her blender?
\newline
_
_
_
_
\_\_\_\_
____
orders
Get tutor help
Philip received a new pie cookbook as a gift and wants to try a new recipe every weekend. There are
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4
kinds of pie he is most interested in making. In how many different orders could he bake all of these pies?
\newline
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_
_
\_\_\_\_
____
orders
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A group of
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5
5
friends found seats in a row at the movie theater. In how many different orders can they sit?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
orders
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