Ice cream&cone combinatorics question 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.

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.