Answer :
To solve the problem of how many possible 4 scoop bowls there are in the ice cream parlour, we need to first understand what the difference between a cone and a bowl means for our calculations.
In the context of this problem:
4 Scoop Cone: The order in which the scoops are placed matters because the ice cream scoops are stacked on top of each other.
4 Scoop Bowl: The order of the scoops does not matter because the scoops are typically side-by-side or mixed, where the arrangement is not significant.
Given that there are 216 possible 4 scoop cones, this number considers each different order as distinct.
If we assume that there are 'n' different flavors of ice cream, each combination of flavors in a cone can be arranged in 4! (which is 24) different ways since the order matters. Therefore, to find the number of combinations for the bowl, where order does not matter, we need to divide the total number of cone permutations by 24.
Let's set up the equation:
[tex]\text{Number of 4 scoop bowls} = \frac{\text{Number of 4 scoop cones}}{4!}[/tex]
[tex]= \frac{216}{24} = 9[/tex]
Therefore, there are 9 possible 4 scoop bowls in the ice cream parlour. This calculation assumes that any combination of flavors is possible and that each combination is unique when order does not matter.
