# 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.

• Just multiply the number of different two-scoop combinations by $3$ – Shubham Johri Jun 4 '19 at 7:22

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.