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Selecting Cereal Boxes Wake Up cereal comes in 2 types, crispy and crunchy. If a researcher has 10 boxes of each, how many ways can she select 3 boxes of each for a quality control test?
Intro Stats / AP Statistics
Chapter 4
Probability and Counting Rules
Section 4
Counting Rules
Sampling and Data
Probability Topics
Temple University
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\text {Solve each problem …
There are two types off wake up cereal, crispy and crunchy. A researcher needs to do a quality control test. She needs to select three boxes from 10 boxes of Krispy cereal and select three boxes from 10 boxes off crunchy cereal. In how many ways can she do this? So the number of ways of selecting three boxes from 10 is given by combination, then taken three. So that applies for both the crispy and crunchy cereal. Now, according to the fundamental counting rule applied to two events. If you have a sequence off to events in which the first event has K one possibilities, the second event escaped two possibilities. Then the total number of possibilities for the sequence will be K one times Kate, too, Right? So the number of ways the researcher can select the boxes that she needs to do the test is going to be given by combination, then taken three times combination, then taken three. Not to evaluate this, um, you can use the combination rule, which states that okay combination and taken our ISS and factorial over and minus r factorial times R factorial they can do. You can use this rule to calculate combination, then taken three, which will be 10 factorial over seven factorial Times Street factorial. You can use your calculator that would be equal to 1 20 Now. Some calculators can calculate combination values directly. Either way, the answer that you would get would be 1 20 times 1 20 which is equal to 14,000 400 different ways.
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