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There are 31 flavours of ice cream and 3 different choices of ice cream cones. How many possible two-scoop ice cream and cone possibilities are there? Consider that a combination of a scoop of vanilla followed by a scoop of chocolate is the same as a scoop of chocolate followed by a scoop of vanilla.

I know how to calculate 31 flavours of ice cream with two-scoop, but I couldn't figure it out with 3 different ice cream cones.

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  • $\begingroup$ Just multiply the number of different two-scoop combinations by $3$ $\endgroup$ – Shubham Johri Jun 4 '19 at 7:22
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You just need a combination of scoops, AND a choice of cone.

The number of ways in which you can do this in $\displaystyle \binom{31}{2}+31$, the number of ways to choose two scoops, times $3$, the number of ways to choose a cone.

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