Question

3. Plonk Winery are packing "mixed dozens" for an upcoming sale. They have available 3 red varieties (Shiraz, Merlot and Cabernet) and 2 white varieties (Riesling and Verdelho). Each mixed dozen must contain 12 bottles, at least two of which must be red, and at least two must be white. (a) How many mixed dozens are possible with these constraints? (b) How many mixed dozens include at least one bottle of each of the 5 varieties? (c) Towards the end of the day, the supply of Merlot runs low. How many mixed dozens are there that contain at most one bottle of Merlot?

Answer 1

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