This is a counting problem that can easily be solved by being systematic, either by making a list or drawing some pictures.
The fact that the two ice cream scoops are side by side in the cone is important. You get a different result if a scoop of ice cream is put on top of another scoop. This is evident in the Solution.
The Sloppy Ice Cream Dairy has four flavours of ice cream. How many different cones can you buy that have two different flavours side by side in the cone?
How many different ice creams can you buy if the scoops of different flavours are placed one on top of the other in the cone?
It is possible to vary these questions by changing the number of ice cream flavours and by changing the number of different flavours that you can have on each cone. Students may agree they can choose the same flavour twice in the same cone.
Suppose the flavours are vanilla (V), chocolate (C), strawberry (S), and boysenberry (B). We must use different flavours in each cone and the different types of ice cream are side by side in the top of the cone. Remember also that the order of the flavours doesn't matter, for example,VC = CV. These are important pieces of information. Here are the possible solutions.
VC VS VB CS CB SB
There are 6 possibilities here.
We’ll do this in the same way. Once again we must use different flavours in each cone but this time, the flavours sit on top of each other. This means that a vanilla scoop on top of chocolate chip scoop is not the same as chocolate chip on top of vanilla. There are 12 possibilities.
C S B V S B
V V V C C C
V C B V C S
S S S B B B
Your class may notice that 12 is twice 6. Is there a reason for this? Look at the list again in a different order.
C V S V B V
V C V S V B
VC VS VB
C S C B S B
S C B C B S
CS CB SB
The different cones are occurring in pairs, two for each of the side by side cones.
Printed from https://nzmaths.co.nz/resource/how-many-ice-creams at 6:38am on the 20th May 2022