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Tino's Ice Cream Shoppe features seven flavors: vanilla, chocolate, pistachio, coconut, blackberry, lemon, and saffron. Tino will gladly make you an ice cream shake featuring any two scoops you want (not necessarily of different flavors). For example, you can order blackberry-vanilla, or pistachio-saffron, or even chocolate-chocolate. Since the scoops are just going into the blender anyway, the order of the scoops doesn't matter: there's no difference between blackberry-vanilla and vanilla-blackberry.

How many different shakes can you order?

 Jan 13, 2019
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\(\text{The number of flavors is }\\ N=7 + \dbinom{7}{2} = 7+21=28\)

 

\(\text{The first 7 are the flavors that are two scoops of a given flavor}\\ \text{The 21 are the unordered pairs of two different flavors}\)

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 Jan 13, 2019

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