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There are 12 cupcakes that will be arranged in a bakery display window. 6 of them...

There are 12 cupcakes that will be arranged in a bakery display window. 6 of them are vanilla flavored, 4 of them are chocolate flavored, and 2 of them are birthday cake flavored. Suppose that each cupcake is decorated differently.

(a) How many ways are there to arrange these cupcakes in the window such that all cupcakes of the same flavor are next to each other?

(b) How many ways can the cupcakes be arranged if one birthday cake flavored cupcake must be on each end of the display and vanilla cupcakes cannot be placed next to birthdaycake flavored cupcakes. (Cupcakes of the same flavor do not have to be placed next to each other.)

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