Question

A server at the Luminous Nose restaurant goes to this same ice-cream store but decides to get a triple-decker cone. The stacking of scoops on the cone is important: a cone with peppermint atop two scoops of squirrel tastes different than a cone with two scoops of squirrel atop a scoop of peppermint, so an order of peppermint-squirrel-squirrel is different from an order of squirrelsquirrel-peppermint. How many possible triple-decker ice-cream orders are there?

Answer 1

Explanation:

Lets rename the variables as

P = peppermint

S = squirrel.

Now, let's see how many different ice cream orders can we made with this two flavours.

We got 3 scoops. So we can place on the first scoop P.

And on top, we can add P P, S S, S P , or P, S.

So the Triple Decker would be ( PPP, PSS, PSP , PPS)

So we can get 4 kind of flavours with Peppermint on the first scoop.

And if we use a scoop of Squirrel on the first level. We would also have

( SPP, SSS, SSP, SPS)

So we can order 8 different ice cream orders. This is called a variation with repetition. And the math function that represents it is:

`2^3`

Where 2 is different variables that we can use (Pepper or Squirrel), and 3 is the number of places where we can place the variable.(the order of the scoop)