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Rule of Sum and Rule of Product

Seek simple and succinct solutions in these systems by sussing-out the significant symmetries.

Rule of Sum

         

A shopping mall has three parking lots. The first parking lot has \(6\) empty parking spaces, the second has \(80\) and the third has \(310.\) If a car comes to the mall, how many choices are there for the car to park in a parking space?

A pet store has \(12\) green frogs, \(10\) black and white dogs, \(8\) brown cats, \(7\) green iguanas, and \(11\) yellow snakes. If you want a pet that is green or brown, how many choices do you have?

On Calvin's street, each house is painted in a single color. There are 6 houses that are painted red, 9 houses that are painted blue, and 12 houses that are painted neither red nor blue. How many houses are there in total?

Carlos went to the climbing gym, which has different types of climbing routes on the various walls. There are 10 top-roping routes on one wall, 6 lead-climbing routes on a second wall, and 9 bouldering routes on a third wall. If Carlos only has time to climb one route before he goes to work, how many choices does he have?

The new books section of the library contains \(7\) different nonfiction books, \(4\) different romance softcovers, \(6\) different mystery hardcovers, and \(5\) different comics. If Anna would like to check out exactly one book from the new books section, how many choices does she have?

Note: These categories are mutually exclusive.

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