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Joy likes six types of bagels: plain, raisin, chocolate, blueberry, egg, and everything. How many different ways are there to choose 6 bagels when she

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Joy likes six types of bagels: plain, raisin, chocolate, blueberry, egg, and everything. How many different ways are there to choose 6 bagels when she can can choose at most two everything bagels? (Assume there is an unlimited supply of each type of bagel.)

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