This is a combination.
You "take" 5 elements among 20 elements (the houses).
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There are two small towns, Greenville and Yellowville. Greenville contains 20 houses and Yellowville contains 15 houses. The state safety inspector is asked to randomly inspect 5 houses in Greenville and 7 houses in Yellowville. In how many ways can this be done (Hint: this is not a permutation)?