Counting Cookies

December 10, 2018

Santiago baked gingerbread cookies in the shapes of children. He gave each gingerbread boy and girl eyes made from chocolate covered candies in one of four different colors, a nose made from a butterscotch chip, toffee chip or peanut butter chip, and a mouth made from a piece of red licorice. Santiago then gave each gingerbread boy and girl buttons made from gum drops in one of four different flavors. For the final detail, he gave each gingerbread boy a blue bow tie, and each gingerbread girl a red hair bow. Based on these options, how many dozens of cookies did Santiago bake if each gingerbread cookie he made was uniquely decorated with a different combination of eyes, nose, mouth, buttons and bow?

 

Suppose that instead of choosing one of the four different gum drop flavors for the buttons, Santiago decided that each gingerbread boy and girl would have three buttons, each made from a different flavored gum drop. If there are four different flavors of gum drops, how many different combinations of three gum drop buttons are possible?

 

How many different arrangements of three buttons can Santiago make using the combinations of three different flavored gum drops from the previous problem?

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