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Question

In a bagel shop that has onion bagels, poppy seed bagels, egg bagels, salty bagels, pumpernickel bagels, sesame seed bagels, raisin bagels, and plain bagels, how many ways are there to select six bagels if the order doesn't matter and repeats are acceptable?

Answer

There are 1716 ways to select six bagels.

Combination is a mathematical operation that counts the number of potential configurations for a set of elements when the order of the selection is irrelevant. In this problem, there are 8 types of bagels (n = 8), and we must select 6 of them without considering the order (Combination) and with repeats allowed. The formula to use is C(n + r-1, r), where n is the number of types of bagels, and r is the number of bagels to be selected. Thus, C(8+6-1, 6) = C(13, 6) = 13!/(7!6!) = 1716. Therefore, there are 1716 ways of selecting six bagels from the given types.