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Counting technique

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11.) 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)?

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This provides an example of determining the number of combinations of house inspections possible.

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Let C(m, n) = n! / (m! * (n-m)!) be the combinatorial number of selecting m items out of n ...

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