SOLUTION: I have a challenge for all of you. Suppose you have a friend named Ed. He and his four friends are having ice cream. There are only three flavors available at the ice cream store t

You did not specify, so I will consider two cones 
with the exact same flavors, but in a different order, 
to be different cones.

That is, say, a 3-scoop cone with strawberry on the bottom,
chocolate in the middle, and vanilla on top is a 
different cone from a 3-scoop cone with vanilla on the 
bottom, strawberry in the middle and chocolate on the
top.  

Do you consider those as different cones?  If you don't,
then the problem is more complicated, so please post 
again, stating that the order in which the scoops are 
stacked on top of the cone does not matter.

Here goes when order of scoops on a cone DOES matter. 

Stacy either has 1 scoop of chocolate, 
2 scoops of chocolate, or 3 scoops of chocolate.
So there are three ways Stacy could order her cone.

For each of those 3 ways Stacy could order her cone,
there are 3 ways Ed could order one scoop.  There
are 3x3 or 9 ways Ed could order two scoops, and 
3x3x3 or 27 ways Ed could order three scoops. That's
3+9+27 or 39 ways Ed could order his cone.

That's 3x39 or 117 ways Stacey and Ed could order their cones. 

For each of the 117 ways Stacey and Ed could order their cones,
the third person could order a cone the same 39 ways
as Ed ordered his cone. 

That's 117x39 or 4563

For each of the 117 ways Stacey, Ed, and the third person
could order their cones, the fourth person could order a 
cone the same 39 ways as Ed and the third person ordered 
their cones. 

That's 4563x39 or 177957

For each of the 177957 ways Stacey, Ed, the 3rd and 4th person
could order their cones, the fifth person could order a 
cone the same 39 ways as Ed, the 3rd and the 4th person could
have ordered their cones.

That's 177957x39 or 6940323 ways.

So you could write



or



Edwin