Calculate Number of Insecticide Tests
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An insect toxicologist would like to test the effectiveness of three new pyrethroid insecticides on population of European corn borer moths, Ostrinia nubilalis, but she has 7 different geographically isolated strains available. If each strain could be used more than once, how many different tests could she perform?
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Let's read this combinatorics problem carefully together. An insect toxicologist is testing three different insecticides on seven different geographically isolated strains of moths. The key detail here is that each strain can be used more than once. We need to find the total number of different tests she could perform.
Permutations with Repetition
To solve this, we should think of each insecticide as an independent decision. We have Insecticide one, Insecticide two, and Insecticide three.
For the first insecticide, how many choices of strains does she have? There are seven available strains.
Because the problem states that each strain can be used more than once, she still has seven options for the second insecticide.
And following the same logic, she has seven options for the third insecticide as well.
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