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The Strategies of Looking for a Pattern and Making an Organized List Practice Questions (page 2)

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Updated on Oct 3, 2011

Practice 2

Try the following practice set. Use the strategy of making an organized list to help find a reasonable answer.

Problems

  1. At an ice cream shop, patrons can select chocolate, strawberry, or vanilla ice cream. They can also select if they want the ice cream in a cone or a dish. If only one flavor can be selected, how many different types of ice cream desserts can be chosen?
  2. Janice can select History, Math, or English for her period 1 class. For her period 2 class, she can select Art, Music, Health, or Science. If she selects exactly one class for each of these periods, how many different combinations of classes are there?
  3. At the Bistro Burger restaurant, a customer can select a plain or sesame roll for their burger. They can also select one of four toppings: ketchup, mustard, mayonnaise, or relish. If a customer selects exactly one type of roll and one topping, how many different burgers can be made?

Solutions

  1. Read and understand the question. The question is asking for the total number of possibilities when selecting one flavor of ice cream and a cone or a dish. There are 3 different flavors and 2 ways to serve the ice cream.
  2. Make a plan. Make a list of all of the combinations of one flavor with a cone or a dish. Then count the total number of possibilities to find the answer.

    Carry out the plan. Make an organized list pairing each flavor with a cone, and then each flavor with a dish. An organized list could appear as follows:

    cone—chocolate dish—chocolate
    cone—strawberry dish—strawberry
    cone—vanilla dish—vanilla

    This is a total of 6 different pairs; therefore, there are 6 different possibilities.

    Check your work. Since there are three flavors paired with a cone or a dish, there should be 3 + 3 = 6 possibilities. This is the same as the number of items in the organized list.

  3. Read and understand the question. The question is asking for the total number of possibilities when selecting from 3 classes for period 1 and 4 classes for period 2.
  4. Make a plan. Make a list of all of the combinations of the period 1 choices with each of the period 2 choices. Then, count the total number of possibilities to find the answer.

    Carry out the plan. Make an organized list pairing the period 1 choices with each period 2 choice. An organized list could appear as follows:

    History—Art Math—Art English—Art
    History—Music Math—Music English—Music
    History—Health Math—Health English—Health
    History—Science Math—Science English—Science

    This is a total of 12 different pairs; therefore, 12 different possibilities.

    Check your work. Since there are 3 period 1 classes being paired with 4 different period 2 classes, there should be 4 + 4 + 4 = 12 possibilities. This is the same as the number of items in the organized list.

  5. Read and understand the question. The question is asking for the total number of possibilities when selecting the one type of roll and one topping.
  6. There are 2 different types of rolls and 4 toppings from which to choose.

    Make a plan. Make a list of all of the combinations of each type of roll with one topping. Then, count the total number of possibilities to find the answer.

    Carry out the plan. Make an organized list pairing each type of roll with each topping. An organized list could appear as follows:

    plain—ketchup sesame—ketchup
    plain—mustard sesame—mustard
    plain—mayonnaise sesame—mayonnaise
    plain—relish sesame—relish

    This is a total of 8 different pairs; therefore, there are 8 different possibilities.

    Check your work. Since there are 2 types of rolls being paired with 4 different toppings, there should be 4 + 4 = 8 possibilities. This is the same as the number of items in the organized list.

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