At the Aftermath Ice Cream Parlour each customer designs their own dessert by choosing three different flavours of ice cream from seventeen available and two different toppings from five available. How many different desserts can be created?

As there are total of 17 flavors of ice cream and when one person wants to select 3 different flavors, the combinations which he can create are $$ 17\cdot16\cdot15 $$. Now, the toppings available are 5 and he has to select 2 different flavors, so the different combinations which can be created are $$ 5\cdot4 $$. Now, the total combinations which can be created are $$ \left(17\cdot16\cdot15\right)\cdot\left(5\cdot4\right)=4080\cdot20=81600 $$ Hence, 81600 different desserts can be created.