An ice cream store sells 30 different flavours of ice cream and it offers a choice of 3 different kinds of cones. In how many ways can we order a dozen two-scoop ice cream cones if any two of them in one order must differ at least by a flavor or by the kinds of cones?

Question

Thanks for your help.

Answer 1

Assuming that strawberry on vanilla is considered the same flavour as vanilla on strawberry, i.e. order of the two scoops doesn't count, then there are 30C2 possible flavours, and 3 cones for a total of n=3(30C2) possible ice creams.

For an order of 12 different ice-creams, there are nC12 possible distinct orders.